Chapter 15 Thermodynamics of gases
Introduction Thermodynamic is the study of the laws that govern the conversion of energy from one form to another, the direction in which heat will flow and the availability of internal energy to do work. 15.1 Heat Capacity Heat capacity, C of an ob!ect is the heat re"uired to raise the temperature of the ob!ect by 1 # $or 1%C&.
The heat, ' re"uired to raise the temperature of a body by (T is given by)
Specific heat capacity, c of a material is the heat re"uired to raise the temperature of 1 kilogram of the material by 1 # $or 1%C&.
The heat, ' re"uired to raise the temperature of m kilogram of a material by (T is given by)
Molar heat capacity, C m of a material is the heat re"uired to raise the temperature of 1 mole of the material by 1 # $or 1%C&.
The heat, ' re"uired to raise the temperature of n mole of a material by (T is given by,
*or gases + as has two heat capacities, one at constant volume and another at constant pressure. + Molar heat capacity at constant volume, C v,m of a gas is the heat re"uired to raise the temperature of 1 mole of the gas by 1 # $or 1 %C& at constant volume. + The heat, ' re"uired to raise the temperature of n mole of a gas by (T at constant volume is given by
+ Molar heat capacity at constant pressure, C p,m of a gas is the heat re"uired to raise the temperature of 1 mole of the gas by 1 # $or 1 %C& at constant pressure. + The heat, ' re"uired to raise the temperature of n mole of a gas by (T at constant pressure is given by + Cv,m and C p,m depend on the degree of freedom. +C-,m
and C p,m
where f is the degree of freedom.
15./ 0ork 0hen a gas epands, work is done by the gas. 0hen a gas is compressed, work is done on the gas.
0hen the gas at constant pressure epends by pushing a light frictionless piston as shown in *igure above the work done by the gas is)
Hence, the work done by a gas when its volume increase from - 1 to -/ is given by
The work done by gas for various types of changes will be discussed in the subse"uent section. The changes involved are) 2 Isobaric change $constant pressure& 2 Isometric change $constant volume& 2 Isothermal change $constant temperature& 2 3diabatic change $no heat flow in or flow out from the system& 15.4 *irst aw of Thermodynamics The first law of thermodynamics is a law of conservation of energy. The first law of thermodynamics states that the heat supplied to a system e"uals to the sum of increase in internal energy of the system and the work done by the system.
The sign convention for ', (6 and 0 used in the formula above is shown below) ' is positive when heat is supplied to the system. ' is negative when heat is released from the system. (6 is positive when the internal energy $temperature& increases. (6 is negative when the internal energy $temperature& decreases. 0 is positive when work is done by the system. 0 is negative when work is done on the system.
15.7 Internal 8nergy The internal energy, 6 of a system is the total potential and kinetic energy of the molecules. *or an ideal gas, because the force between the molecules is negligible, the potential energy e"ual 9ero. The internal energy is the total kinetic energy of the molecules only. #inetic energy $internal energy& for one mole of gas
kinetic energy
$internal energy& for n mole of gas $n& The internal energy of the ideal gas depends on) $a& 3mount of gas $number of moles& $b& 3bsolute temperature $c& :egree of freedom 0hen temperature of gas increases, internal energy increases and (6 is positive. 0hen temperature of gas decreases, internal energy decreases and (6 is negative.
15.5 Isometric Change 3n isometric process is a constant;volume process.
To raise the temperature of n mole of gas by (T at constant volume, the heat re"uired
15.= Isobaric Change 3n isobaric process is a constant;pressure process.
To raise the temperature of n mole of gas by (T at constant pressure, the heat re"uired
15.> relation between C v,m and C p,m
The ratio of
+Internal energy for n mole of gas at temperature T +Change in internal energy for n mole of gas when there is a temperature change of (T
so
and
+The ratio of C p,m to C-,m is denoted by ?
@ote) C-,m can also be obtained from the definition
-alues of C p,m , C-,m and ? at a glance :egree of freedom at room temperature C-,m
:iatomic
Bolyatomic
C p,m C-,m D ?
Aonoatomic
15.E Isothermal Change 3n isothermal process is a constant;temperature process.
3n isothermal change obeys FoyleGs law. *or an isothermal change, the gas must be held in a thin;walled, highly conducting vessel, surrounded by a constant temperature bath. The change must take place slowly so that heat can flow into the gas or flow out from the gas to maintain its temperature at every instant during the change.
0ork done in an isothermal change +0ork done by gas in an isothermal change is given by 0 +6sing the ideal gas e"uation p- nT
l5. 3diabatic Change
3n adiabatic process is a process where no heat is transferred into or out of the system.
:uring an adiabatic epansion, 0 is positive and (6 is negative. i.e. during adiabatic epansion, internal energy decreases and temperature decreases. :uring an adiabatic compression, 0 is negative and (6 is positive. i.e. during adiabatic compression, internal energy increases and temperature increases. 3n adiabatic change observes the following e"uations)
*or an adiabatic change, the gas must be held in a thick;walled, badly conducting vessel. The change must take place rapidly so that there is little time for the heat to escape. The magnitude of gradient of the adiabatic curve is greater than that of the isothermal. 3diabatic e"uation + Ideal gas e"uation +*irst law of thermodynamics +3diabatic change +Change in internal energy +0ork done +elation between + *rom
@ote) 0ork done for adiabatic change may also be obtained directly from change in internal energy if the temperatures are known.
