Exams › JEE Advanced › Chemistry
During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. Find the ratio Cp / Cv for the gas.
- 3/2
- 7/5
- 5/3
- 4/3
Correct answer: 3/2
Solution
For an adiabatic process: TV^(gamma-1) = const and PV^gamma = const. Using PV = nRT, we can eliminate V. From PV = nRT: V = nRT/P. Substitute into PV^gamma = const: P*(nRT/P)^gamma = const => P^(1-gamma)*T^gamma = const. Given P proportional to T³, so P = k*T³, i.e., T proportional to P^(1/3). From adiabatic: T^gamma / P^(gamma-1) = const => T proportional to P^((gamma-1)/gamma). So (gamma-1)/gamma = 1/3 => 3(gamma-1) = gamma => 3*gamma - 3 = gamma => 2*gamma = 3 => gamma = 3/2.
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