Between two isotherms at temperatures 2T and T, a process ABCD is performed with an ideal
monatomic gas. AB and CD are adiabatic expansion processes and BC is isobaric expansion
process. The average molar specific heat capacity of the overall process will be
A -3R/2
B 5R/2
C 3R/2
D -5R/2
Answers
Given:
A process ABCD is performed with an ideal monatomic gas between two isotherms at temperatures 2T and T.
AB and CD are adiabatic expansion processes and BC is an isobaric expansion process.
To Find:
The average molar specific heat capacity of the overall process
Solution:
The average molar specific heat capacity of the overall process is D) -5R/2.
An isothermic process is one in which the temperature of the surroundings is always constant.
The net heat exchanged during the overall process Q = Qab + Qbc + Qcd
Since it is given that AB and CD are adiabatic expansion processes
⇒ No heat is exchanged during these processes
⇒ Qab = Qcd = 0 J.
∴ Q = Qbc
The heat exchanged during an isothermic process = nCpΔT.
Here, n is the number of moles of the ideal gas, Cp is the molar heat capacity at constant pressure and ΔT is the temperature difference.
Substituting the values,
Q = Qbc = nCp (Tc - Tb)
or Q = Cp (2T- T)
= CpT - (1)
(Taking n = 1 since we need to calculate the average capacity)
Let the average molar specific heat capacity of the overall process = C
According to the formula, Q = n C (Ta-Td)
= C (-T) - (2)
Equating equations 1 and 2,
-C T= Cp T
or C = - Cp
For a monoatomic gas, the value of Cp = 5R/2