MODULE 2

HEAT

Learning Outcomes:

Describe the effect of thermal expansion
Explain the basic concepts of heat transfer by conduction. convection and radiation
Study the heating and cooling of a pure substance through a change of phase
Use the ideal gas laws to calculate change in pressure , temperature and volume

2.1 Heat energy

Heat, in science, is defined as the energy which is transferred from a body at a higher temperature to one at a lower temperature by conduction, convection or radiation. Like other forms of energy it is measured in joules, J.

When a transfer of heat occurs the internal energy of the body receiving the heat increases and if the kinetic component increases, the temperature of the body rises.

Heat is concern with energy in the process of transfer and when the transfer is over, the term is irrelevant. Thus, the expression 'heat in a body', although often used, is misleading. We should talk about the 'internal energy' of the body.

2.1.1 Thermometer

A thermometer is any instrument which is used to measure the temperature of a system. All thermometers are based on the principle that some physical property of a system changes continuously with the system’s temperature.

The thermometer needs a scale to be used effectively. To construct a temperature scale, two fixed points must first be obtained. These two fixed points are called lower fixed point and upper fixed point. The lower fixed point is the temperature of pure melting point at standard atmospheric pressure. This temperature is called the ice point. And the upper fixed point or the steam point is the temperature of dry steam from water boiling at standard atmospheric pressure. In the case of the Celsius scale, the length between the two points is divided into 100 equal divisions. It means the physical property varies uniformly with temperature.

Figure 2.1 Thermometer

2.1.2 Scales of temperature

The Celsius Scale

This scale is named after the Swedish astronomer Anders Celsius. On the Celsius temperature scale, the ice point is assigned a value of zero degrees Celsius (0°C) and the steam point is assigned a value of 100°C. The distance between the ice point and the steam point is divided into 100 equal segments to create the Celsius scale. Thus, each segment is a measure of 1°C.

The Fahrenheit Scale

This scale was devised by the German physicist, Daniel Gabriel Fahrenheit. This scale sets the temperature of the ice point at 32°F and the temperature of the steam point at 212°F. The relationship between the Celsius and Fahrenheit temperature scales is

TF= (9/5 × TC) + 32°

The Kelvin Scale

The Kelvin scale is the SI unit of absolute temperature. This scale was devised by the English scientist Lord Kelvin. The Kelvin scale is based on a true zero value (absolute zero) of temperature. Absolute zero corresponds with - 273˚ on the Celsius scale. The ice-point temperature on the Kelvin scale, 273 K, corresponds to 0.00°C, and the Kelvin-scale steam point, 373 K, is equivalent to 100.00°C.

The relationship between the Celsius and Kelvin scales is

T = TC+273

Where TC is the Celsius temperature and T is the absolute temperature.

The size of a degree on the Kelvin scale is identical to the size of a degree on the Celsius scale.

2.1.3 Specific heat capacity

Materials differ from one another in the quantity of heat needed to produce a certain rise of temperature in a given mass. The specific heat capacity c enables comparisons to be made.

If a quantity of heat Q raises the temperature of a mass m of material by t, then c is defined by the equation

2.1.4 Heat capacity

The heat capacity or thermal capacity of an object is defined as the quantity of heat needed to produce unit rise of temperature in the object. It is measured in joules per Kelvin ( or joules per degree Celsius).

From the definition of specific heat capacity, we have:

Heat capacity = mass x specific heat capacity

Thus the heat capacity of 10 kg of aluminium (specific heat capacity 910 J kg-1K-1) is 9100 J K-1.

2.2 Expansion of Solids and Liquids

2.2.1 Thermal Expansion

A solid expands as it is heated because the amplitude of molecular vibration increases with the increase in temperature. A similar effect occurs in liquids. The expansion of liquids per degree rise in temperature is generally about ten times as large as the expansion of solids.

Effects of thermal expansion are exceedingly important. Building materials, structural components, machine parts – all materials change in size when they experience a change in temperature. Serious problem can result if these dimensional changes are not anticipated. Expansion joints must be included in the design of long sections of pipelines and sidewalks. Sufficient clearance must be provided between moving machine parts so that the parts will not seize when a change in temperature occurs.

Linear Expansion of Solid Materials

Different materials expand or contract at different rates. The magnitude of the linear expansion or contraction, l, of a solid material depends upon three factors:

(i) the linear dimension, lo, of the material – the bigger the original dimension, the more it will expand or contract;

(ii) the temperature change Δ T - the larger the change in temperature, the greater the expansion or contraction;

(iii) the coefficient of linear expansion, δ - a property of the solid material.

Therefore, the coefficient of linear expansion is the fractional change in length per degree change in temperature. The term linear refers to any straight-line dimension of a body. Though the change is very small, the forces set up can be tremendous if allowance is not provided for the expansion or contraction to take place.

Typical values of the coefficient of linear expansion for a selection of materials are shown below:

Bimetallic Strip

One example of expansion that has many application is shown below, where strips of brass and steel are riveted together. The expansion of brass is nearly twice that of steel for a given increase of temperature. Consequently, when the bimetallic strip is heated, it bends into an arc.

A device that makes good use of the bimetallic strip is the thermostat. It is used to turn equipment on or off depending on the temperature. As the strip is heated, it tends to become curve rather than straight. The free end of the strip is forced up and the two upper contact points touch. As the strip is cooled, the brass contracts more than the steel. The free end of the strip bends down, separating the two upper contact points. As the strip is cooled further, it bends down still more until the two lower contact points are touching.

The thermostat can be used to operate a device such as a heater that heats a room. As the temperature of a room drops, the strip bends down until the bottom contacts touch. By means of a suitable electrical circuit, when these contact points touch, a relay operates that, in turn, closes a switch that starts a heater. The temperature at which the contact points touch may be regulated by the bottom adjustment screw that sets the contact points closer together or farther apart.

As the heater heats the house, the strip starts to bend up. The two bottom contact points are separated, but the heater continues to raise the temperature until the two upper contact points touch. This operates a second relay, which turns the heater off. The upper adjustment screw regulates the temperature at which the heater is turned off. The heater remains off until the temperature drops sufficiently for the two bottom contact points to touch once again.

Negating the Effect of Expansion

The effects of linear expansion must be reckoned with constantly throughout industry. In oil-field piping and in the plumbing, refrigeration and steam-fitting trades, careful attention must be given to providing expansion joints at the right places. In bridge and building construction, expansion joints must be provided for each major section.

2.2.2 Superficial Expansion of a Solid

The amount by which unit area of a material increases when the temperature is raised by one degree is termed the coefficient of superficial expansion and is represented by the Greek letter β.

2.2.3 Cubic Expansion of Solids and Liquids

The amount by which unit volume of a material increases for one degree rise of temperature is termed the coefficient of cubic expansion, and is represented by the Greek letter r.

It is this peculiar behaviour of water that causes lakes and oceans to freeze on top first, rather than at lower levels. Consider a body of water as winter sets in. The warmer water, being less dense, continually rises to the top, and a steady circulation is maintained until the entire body of water reaches a temperature of 4P oPC. Below this temperature the colder water is less dense and stays on top, where it quickly freezes. Extremely cold weather is required to freeze a layer as much as 30 cm thick, since ice is a poor conductor of heat.

2.3 Heat Transfer

There are many situations where heat must be transferred from one place to another. Steam heat is used in many industrial processes. Heat must be removed from a refrigerator and radiators are used to heat rooms. Heat transfer has many practical applications and we shall examine some of them in this chapter.

There are three basic ways in which heat energy is transferred from place to place. They are conduction, convection and radiation.

2.3.1 Heat Transfer by Conduction

When a flame heats one end of a metal rod, it gives energy to the atoms at that end of the rod. This causes the atoms to vibrate with more and more energy. But by collision with their neighbouring atoms, they share this energy with their cooler neighbours. These atoms in turn strike their neighbours and pass energy along to them. In this way thermal energy is transferred from atom to atom along the rod and so the whole rod becomes warm.

Hence, heat transfer by conduction is the transfer of heat energy from particle to particle by direct collision of the particles.

Metals are better conductors of heat as compared to wood or plastic. This is due to the fact that metals contain many free electrons. The free electrons as well as the atoms undergo collisions and thereby aid in transporting the heat.

To categorise the good conductor and bad conductor (insulator) of heat, we define a quantity called the thermal conductivity. To define it, we consider a slab of material such as the one shown below. Its thickness is L and its face area is A. If a temperature difference T2-T1 exists between its faces, then heat will flow through the slab.

The heat flow per unit time, through the slab is given by :

2.3.2 Heat transfer by Convection

Thermal energy can be moved from place to place by moving the molecules themselves. For example, hot air can be blown into a room to heat it. Hot water can be sent through a pipe to heat an object. Unlike conduction, heat energy is not transported by collision. It is transported by the movement of the molecules themselves over large distances. We call this type of heat transport convection.

2.3.3 Heat Transfer by Radiation

The two heat transfer methods, conduction and convection, make use of molecules. The third method by which energy is carried from hot to cold objects is quite different. It does not use molecules to carry the energy. In this process, radiation moves energy through a vacuum.

Heat energy as well as light travels from the sun to the earth. The space between the sun and the earth is a vacuum.

All objects are continuously emitting heat energy. At low temperature the rate of emission is small. As the temperature is increased, the rate of emission increases very rapidly. Experiment has shown that the rate at which thermal energy is radiated from a surface varies directly with the fourth power of the absolute temperature (in degree Kelvin) of the radiating body. The rate of heat transfer by radiation also depends on the nature of the exposed surfaces. Objects that are good emitters of thermal radiation are also good absorbers of radiation. Dull and black objects are excellent emitters and absorbers of radiation.

Questions and problems

Exercise 1

A square slab of a thickness of 4 cm and measuring 25 cm on a side has a 40°C temperature difference between its faces. How much heat flows through it per hour? The thermal conductivity is 1.05 W m-1 °C-1. [236.25 kJ]

Exercise 2

An ordinary refrigerator is thermally equivalent to a box of corkboard 90 mm thick and 5.6 m2 in inner surface area. When the door is closed, the inside wall is kept, on the average, 22.2°C below the temperature of the outside wall. At what rate must heat be removed by the motor from the interior? The thermal conductivity of corkboard is 0.05 Wm-1K-1. [ 69.06 W ]

Exercise 3

A 1 m2 glass windowpane has its outside surface at 20oC when the air temperature far away from the window is 5oC. If the wind speed is 5 m s-1 and the appropriate convection constant tables show that the value of h is 23 W m-2 oC-1 in this case, find the rate of heat transfer. [345 W]

Exercise 4

A dirty solid aluminium sphere (m=11.3 g, area =12.5 cm2) has a temperature of 427oC. What is the rate of loss of heat through radiation? Assume e = 0.60 for the sphere.[ 10.2 W ]

We have said that all object continuously emit radiation, regardless of their temperature . If this is true, why don’t the object eventually run out of energy? The answer is that they would run down if no energy were supplied to them.

The filament in an electric bulb cools quickly to room temperature when the supply of electric energy is shut off. It is emitting heat energy. In other words, abody at the same temperature as its surroundings radiates and absorbs heat at the same rates. That is:

Exercise 5

Repeat Exercise 4, given that the surrounding temperature is 27 oC , 35 oC.[9.86 W, 9.83 W ]

Exercises - Heat transfer

Calculate the rate of heat transfer by conduction through a piece of wood of area 2 m2 and thickness 0.03 m if the temperature difference on the two sides is 10 oC. Given that the coefficient of thermal conductivity for wood is 0.10 W m1oC-1. [ 66.7 W ]
A glass window pane has an area of 2 m2 and a thickness of 0.4 cm. If the temperature difference between its faces is 25 oC, how much heat flows through the window per hour? Thermal conductivity of glass is 8 x 10-3 W cm-1oC-1. [ 3.6 x 107 J ]
A flat vertical wall 6 m2 in area is maintained at a constant temperature of 116oC and the surrounding air on both sides is at 35 oC. How much heat is lost from the wall in 1 hour by natural convection? (h for the vertical wall is 5.32 W m-2°C1). [1.86 x 107J ]
A piece of metal plate measuring 3 m by 4 m is heated to a temperature of 500oC. If heat is lost by radiation from both sides of the plate, calculate the rate of heat loss. Take the value of e to be 0.9 for the metal plate. What is the likely colour of the metal plate? [ 4.37 x 105 W, nearly black ]
The surface of the sun has a temperature of about 5800 K. Taking the radius of the sun to be 6.96 x 108 m, calculate the total power radiated by the sun. [3.9 x 1026 W]
Assuming that the approximate value for the surface area of the human body is 1 m2 and its thermal emissivity is 1.0, calculate how much heat energy is radiated away in 24 hours, assuming the body temperature to be 37oC and room temperature to be 22oC. [ 8141 kJ ]
An aluminum saucepan with a metal handle is full of water and is covered with a lid. The saucepan is being heated on a electric hot-plate, slightly smaller than the base of the saucepan. What are the process(es) of heat transmission in

(a) heating the base of the saucepan?

(b) distributing the heat through the water?

2.4 Change of State

A substance may exist in any one of three phases, that is, as solid, liquid or gas.

The differences between the three phases of matter can be explained by simple kinetic theory. In a solid, the molecules are very close to one another arranged in a fixed pattern and merely vibrate about their constant mean positions due to strong attractive forces between them. Hence a solid has a definite volume and shape.

In a liquid, the molecules have greater kinetic energy to move more freely but the forces of attraction between them are still fairly strong. A liquid still has a definite volume but no definite shape. In contrast, a gas neither has a definite volume or a definite shape. This is due to greater energy possessed by the molecules in a gas that enables them to overcome the attractive forces acting between them.

It is clear that the amount of energy possessed by the molecules determine the phase of the substance. In other words a substance can change its phase by heating or cooling.

2.4.1 Sensible heat and latent heat

Sensible heat is that heat involved when there is a temperature change in a substance. Calculations involving sensible heat use the specific heat capacity equation. That is, the heat required to raise the temperature of a substance of mass m kg and specific heat capacity c J kg-1K-1 is given by :

Q = m c (t2 - t1)

When a substance changes phase (solid to liquid or liquid to vapour) heat energy must be supplied to effect the change. During the change of phase there is no change of temperature. The heat required to change the phase of a substance is known as latent heat.

Temperature-time graph for change of phase

Consider the heating of a piece of ice at –20°C to steam at 120°C. A graph showing the temperature at various times is shown in Fig. 3.1.

Sensible heat is supplied to raise the temperature of ice from -20oC to 0oC (melting point) as shown by portion A to B of the graph. When melting commences, the energy gained is offset by the energy required for the change of phase and the temperature remains constant (B to C).

When all the ice has melted into water the temperature begins torise again(C to D) as sensible heat is supplied. Eventually the water begins to vaporise at 100oC (boiling point). Once again, during this period of transition (D to E), the temperature remains constant. The temperature will rise again when all the water has changed completely into steam and the steam is trapped in the container.

The kinetic theory sees the supply of latent heat to a melting solid as enabling the molecules to overcome the forces between them for the regular crystalline structure of the solid to be broken down. The molecules then have the greater degree of freedom and disorder that characterize the liquid phase.

Thus while heat which increases the kinetic energy component of molecular internal energy causes a temperature rise, the supply of latent heat is regarded as increasing the potential energy component.

When vaporization of a liquid occurs a large amount of energy is needed to separate the molecules and allow them to move around independently as gas molecules. In addition some energy is required to enable the vapour to expand against the atmospheric pressure. The energy for both these operations is supplied by the latent heat of vaporization and is an increase in the potential energy of the molecules.

2.4.2 Specific latent heat of fusion

Specific latent heat of fusion of a substance is defined as the quantity of heat required to change unit mass of the substance from solid to liquid (or vice versa) without a change of temperature. It is denoted by the symbol Lf and its unit is joule per kilogram (J kg-1).

Therefore, the heat involved in the change from solid to liquid (or vice versa) of m kg of a substance with specific latent heat of fusion Lf is :Q = m Lf

2.4.3 Specific latent heat of vaporization

Specific latent heat of vaporization of a substance is defined as the quantity of heat required to change unit mass of the substance from liquid to vapour (or vice versa) without a change of temperature. It is denoted by the symbol Lv and its unit is also joule per kilogram (J kg-1).

Similarly, the heat involved in the change from liquid to vapour (or vice versa) of m kg of a substance with specific latent heat of vaporisation Lv is :

Q = m Lv

2.5 Evaporation

The process of changing the water into vapour without boiling is called evaporation. Evaporation can take place at all temperatures. In the evaporation process, heat from the surrounding is absorption by liquid. Then, the molecules of the liquid gain energy and move faster with different speed. Some of the faster-moving molecules penetrate the surface and leave the liquid by escaping from the attraction of their neighbours.

Consequently, only the molecules of lower average kinetic energy are left behind in the liquid. As a result, the temperature of the liquid decreases. Hence, evaporation gives rise to cooling.

Water is transferred from the surface to the atmosphere through evaporation. Approximately 80% of all evaporation is from the oceans, with the remaining 20% coming from inland water and vegetation. Winds transport the evaporated water around the globe, influencing the humidity of the air throughout the world. Most evaporated water exists as a gas outside of clouds and evaporation is more intense in the presence of warmer temperatures. The strongest evaporation was occurring over the oceans and near the equator.

Averaged across the entire Earth, water evaporates from the surface at a rate of about 3 millimeters per day (about 1/8 of an inch). Over the tropical oceans, the value is much larger; over cold surfaces, it is much lower; and over deserts it is almost zero, since there is little or no water to evaporate. Evaporation from the ocean surface is the primary source of energy for hurricanes.

Table below shows the specific latent heat of fusion and vaporization for some common substances.

Questions and problems

A steel component is quenched (i.e. cooled rapidly in a water bath). The component has a mass of 1.7 kg and its initial temperature is 850 oC. Determine the quantity of heat energy given up to the water if the final temperature of the component and water is 25 oC. The specific heat capacity of steel is 494 J kg-1oC-1. [ 692.8 kJ ]
An electric kettle contains 1.5 kg of water initially at a temperature of 30 oC. If the mass of the kettle is 0.8 kg, calculate the quantity of heat required to raise the temperature of the water to boiling temperature. Assume negligible heat loss to the surrounding.

Given: specific heat capacity of water = 4.20 kJ kg-1oC-1

specific heat capacity of kettle material = 0.45 kJ kg-1oC-1[ 466.20 kJ ]

A large aluminium container has a mass of 350 kg and holds 1500 kg of water, both container and water being at a temperature of 15oC. Assuming that there is no heat loss, what amount of heat transfer is required to raise the container and its contents to a temperature of 87oC? Take the specific heat capacities of aluminium and water to be 946 J kg-1oC1 and 4200 J kg-1oC-1 respectively.[ 477.4 MJ ]
Calculate the heat required to convert 8kg of water at 100 oC into steam at the same temperature. Assume the change of phase takes place at atmospheric pressure and that the latent heat of vaporization of water is 2257kj kg-1 . [18056kj].
When 5 kg of magnesium were raised in temperature from 20oC to 250oC it was found that he necessary heat transfer to the metal was 1200 kJ. Calculate the specific heat capacity of magnesium. [1043 J kg-1oC-1]

Latent heat and specific heat

6. 12 kg of aluminium initially at 25 oC is to be melted. If the melting point of aluminium is 660oC and its specific heat capacity is 946 J kg-1K-1 and its specific latent heat of fusion is 396 kJ kg-1. Calculate the amount of heat energy required. [11.96 x 106 ]

7. Calculate the amount of heat required to generate 5 kg of steam at 100oC and standard atmospheric pressure when the feed water is at a temperature of 10oC. Take the specific heat capacity of water as 4.19 kJ kg-1K-1and the specific latent heat of vaporization of water as 2257 kJ kg -1. [ 13.2 MJ ]

8. Given a mass of 1 kg of ice at –50 oC, determine the quantity of heat needed to change:

(a) the temperature of the ice from –50 oC to its melting point [ 107 kJ]

(b) the ice into water at 0 oC [335 kJ]

(d) the water at 100 oC into steam at 100 oC [2257 kJ]

(e) the temperature from its boiling point to steam at 125 oC [50 kJ]

(f) the temperature from –50 oC to 125 oC [3169 kJ]

Assume the following:

specific heat capacity of ice = 2.14 kJ kg-1K-1

specific latent heat of fusion of ice = 335 kJ kg-1

specific heat capacity of water = 4.2 kJ kg-1K-1

specific latent heat of vaporization of water = 2257 kJ kg-1

specific heat capacity of steam = 2 kJ kg-1oC-1

9. An immersion heater is placed into 1 kg of water initially at a temperature of 25oC.

The temperature of the water rises to 100oC in 315 seconds and the water starts to boil.

Calculate (a) the power of the heater, (b) the time taken for all the water to boil away.

Given: specific heat capacity of water = 4.2 kJ kg-1oC-1

specific latent heat of steam = 2257 kJ kg-1oC-1 [ 1000 W, 37.7 min ]

10. An electric heating coil supplies 50 W of power to raise the temperature of a block of metal, mass 0.60 kg from 25oC to 50oC in 90 s. Neglecting heat loss to the surrounding, calculate the specific heat capacity of the metal. [ 300 J kg-1oC-1 ]

11. How much heat energy is required to change 10kg of ice at 0° C into steam at 100° C at atmospheric pressure? The specific heat capacity of water is 4200 J kg-1 K-1; the specific latent of fusion of ice is 335 kJ kg-1 and the specific latent heat of vaporization of water is 2257 kJ kg-1. ( 30.12 MJ)

2.6 Gases

Expansion of a gas is not as simple as the expansion of a liquid or solid. When dealing with a fixed mass of gas, there are always three factors to consider: pressure, volume and temperature. A change in one of these factors produces a change in at least one of the others. Often all three change at once. This happens, for example, when a balloon rises through the atmosphere.

When a fixed mass of gas at constant temperature changes from state 1 (pressure p1 and volume V1) to state 2 (pressure p2 and volume V2), then according to Boyle's law:

p1V1 = p2V2

2.6.2 Charles' law

2.6.3 Pressure Law

In practice, adiabatic process can be achieved by using a perfect heat insulating material for containing the gas. Another way is to carry out the process very rapidly so that there is very little time for heat enter or leave the gas.

Air escaping from a pressurized tire, causing the valve to become cooler, is an example of adiabatic expansion.

In refrigerators and other cooling systems a fluid is allowed to undergo adiabatic expansion through a throttle valve made of porous plug leading into a low pressure region. The region around the valve is insulated to ensure that no heat is exchanged. Thus, the temperature of the expanded fluid is much lower than its temperature on the high pressure side before it expands.

2.6.6 Refrigeration

Refrigeration means removal of heat. Heat energy always flow naturally from a warmer place to a cooler place. A refrigerator is a device which by means of a motor takes heat energy from a cooler region (inside the refrigerator) to a warmer region (outside the refrigerator).

In a home refrigerator, heat is removed from its storage compartment and freezer and released into the kitchen. The substance used to convey the heat is called a refrigerant.

In modern refrigerators, the most common refrigerant is Freon-12. At one atmospheric pressure (1.0 x 105 Pa), Freon-12 boils at -29.8oC. At 7.5 times the atmospheric pressure (7.5 x 105 Pa), Freon-12 boils at about 37.8oC and is therefore a liquid at room temperature.

To analyze the operation of the refrigerator, let us start at the compressor. The compressor takes in Freon-12 vapour at slightly above atmospheric pressure and at room temperature and compresses it to high pressure of 7.5 atm. This causes the temperature of the Freon-12 vapour to increase.

The hot vapour under high pressure then moves on to the condenser. Air or another fluid (usually water) circulates around the condenser to remove heat from the vapour. The temperature of the Freon-12 vapour decreases below its boiling point of 37.8oC and condenses into a liquid.

The condensed Freon-12 (under high pressure) is then released into a low pressure region by a throttle valve. Some of the liquid vapourises, cooling the rest. The vapour formed undergoes adiabatic expansion into the low pressure region further cooling the liquid-vapour mixture.

As the liquid vapour mixture moves through the evaporator (inside the refrigerator), it absorbs heat and is converted to vapour at a temperature above its boiling point and at low pressure.

The vapour then enters into the compressor, and the cycle repeats.

Questions and problems

Exercise 1

A gas occupies a volume of 0.10 m3 at a pressure of 1.8 MPa. If the temperature remains constant, determine

(a) the pressure if the volume is changed to 0.06 m3.

(b) the volume if the pressure is changed to 2.4 MPa.[ 3 MPa, 0.075 m3 ]

Exercise 2

In an isothermal process, a mass of gas has its volume reduced from 3200 mm3 to 2000 mm3. If the initial pressure of the gas is 110 kPa, determine the final pressure. [176 kPa ]

Exercise 3

A gas occupies a volume of 1.2 litres at 20 oC. Determine its volume at 130 oC if the pressure is kept constant. [1.65 litres]

Exercise 4

A gas at a temperature of 150 oC has its volume reduced by one third in an isobaric process.Calculate the final temperature of the gas. [ 9 oC ]

Exercise 5

If the air ttrapped in a container has a pressure of 3 atm at 27°C, find the pressure when it is heated to 127°C. [4 atm]

Exercise 6

A gas occupies a volume of 2.0 m3 when at a pressure of 100 kPa and a temperature of 120 oC. Determine the volume of the gas at 15 oC if the pressure is increased to 250 kPa. [ 0.586 m3 ]

Exercise 7

A 20,000 mm3 of air initially at a pressure of 600 kPa and temperature 180 oC is expanded to a volume of 70,000 mm3 at a pressure of 120 kPa. Determine the final temperature of the air. [317.1 K]

Exercise 8

A gas undergone adiabatic compression had its volume changed from 0.15 m3 to 0.03 m3. The initial pressure is 140 kN m-2 and the adiabatic index is 1.2. Determine the final pressure. [ 966 kN m-2 ]

Exercise 9

In a refrigerator, Freon-12 gas at a pressure of 10 atm and 20 oC is adiabatically expanded at the throttle valve to one and a half times its volume. Calculate: (a)the new pressure (b) the new temperature and (c) the drop in temperature during the expansion. Assume that is 1.3. [ 5.9 atm, 259 K, 34 K ]

Exercises

Properties of gases
Given: 1 atmospheric pressure = 101.3 kPa

A sealed tank contains oxygen at 27 °C and a pressure of 2.00 atm. If the temperature increases to 100 °C, what will the pressure inside the tank be? Assume that there is no change in volume.[ 2.49 atm ]
A balloon filled at 27 °C, has a radius of 10 cm. If the balloon is taken outside on a winter’s day when the temperature is –23°C, what is its new radius? [ 9.4 cm ]
A 6 litre container holds a sample of gas under pressure of 600 kPa and a temperature of 57°C. What will be the new pressure if the same sample of gas is placed into a 3 litre container at 7°C? [ 1018 kPa ]
An air compressor takes in 2 m3 of air at 20 °C and atmospheric pressure (101.3 kPa). If the compressor discharges into a 0.3 m3 tank at a pressure of 1500 kPa, what is the temperature of the discharged air? [ 650.8 K ]
A metal container, 10.0 cm x 6.0 cm x 2.0 cm, is heated to 100 °C with its cover off. It is then closed tightly, and the container is allowed to cool to room temperature. Calculate the pressure inside the container at room temperature, 27°C. Calculate too the force acting on the surface of the container at room temperature. [ 81.5 kPa , 1.5 kN ]
One litre of nitrogen (for which g = 1.40) at 300 K and atmospheric pressure is compressed adiabatically to one-tenth its original volume, to 0.1 litres. Compute: (a) the final pressure of the gas (b) the final temperature of the gas [2544.5 kPa, 753.6 K ]
A gas occupies a volume of 2.0 m3 when at a pressure of 100 kPa and a temperature of 120oC. Determine: (a) the mass of the gas (b) its volume at 250 kPa and 15 oC

Given R = 184 J kg-1 K-1 [ 2.766 kg, 0.586 m3 ]

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