Question

A monoatomic ideal gas, initially at temperature T1 is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T2 by releasing the piston suddenly. L1 and L2 are the lengths of the gas column before and after expansion respectively, then T1/T2 is given by?

(a) (L1/L2)^(2/3)

(b) L1/L2

(c) L2/L1

(d) (L2/L1)^(2/3)

This question was addressed to me by my college professor while I was bunking the class.

This intriguing question originated from Thermal Equilibrium topic in section Kinetic Theory of Gases of Engineering Physics I

Answer 1

Correct answer is (d) (L2/L1)^(2/3)

For explanation I would say: For an adiabatic expansion,

(TV)^(γ-1)=constant

\(T_1 V_1^{γ-1}=T_2 V_2^{γ-1}\)

For a monoatomic gas, γ=5/3

If A is the area of cross-section of the piston, then

T1/T2 =(V2/V1)^(γ-1)

T1/T2 =((AL2)/(AL1))^(2/3).