Q. 38

An amount n (in moles) of a monatomic gas at an initial temperature T0 is enclosed in a cylindrical vessel fitted with a light piston. The surrounding air has a temperature Ts(>T0) and the atmospheric pressure is pa. Heat may be conducted between the surrounding and the gas through the bottom of the cylinder. The bottom has a surface area A, thickness x and thermal conductivity K. Assuming all changes to be slow, find the distance moved by the piston in time t.

Answer :


In time dt, heat transfer through the bottom of the cylinder is given by-

= (1)

In case of monoatomic gas, pressure remains constant.

Hence the heat content at constant pressure(enthalpy) is given by

dQ=nCpdT (2)


dQ=change in heat

n = number of molecules

dT = change in temperature

Cp = amount of heat required to raise the temperature of a substance of 1Kg mass by one degree Celsius at constant pressure.

Comparing above equations-


For a monoatomic gas, Cp=52 R




Integrating both the sides, we get



ln( =-

Taking antilog


T =


T- = ) (1)

Now, we know the gas equation given by


Substituting in (1)

= T- = )

Solving for the length/distance,

l = )

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