An ideal monatomic gas is contained in a piston whose state is characterised by

Question

An ideal monatomic gas is contained in a piston whose state is characterised by the extensive parameters (U0 ,S0 ,V0 ,N0 ) and intensive parameters (T0 ,P0 , u0 ) . The system is placed in thermal contact with a heat reservoir at constant temperature T0, hence, all processes are isothermal. The plunger in the piston moves slowly out of the piston so that the gas expands quasi-statically to a final volume which is twice the initial volume, Vf= 2V0 .

(i) Calculate the work done by the gas as it expands from V0 toVf= 2V0 .

(ii) Prove that the internal energy U does not change during this expansion.

(iii) Calculate the amount of heat into the gas during this isothermal expansion.

(iv) Calculate the change in entropy that occurs during the expansion.

(v) What is the source of this entropy increase?

Explanation / Answer

i)

Work done by gas in an isothermal process= nRT lnVi/Vf = N0RT0 ln(1/2)

ii)

Since the change is isothermal,

Uf=U0

Change in internal energy =0

iii)

From conservation of energy,

dq+dw=du

Since, du=0...................(from ques. ii)

dq=-dw

Amount of heat into the gas= N0RT0 ln(1/2)

iv)

Since, the process is isothermal,

dS=dq/T

Change in entropy=N0R ln(1/2)

v)

The source of this entropy is the heat exchanged at the boundary of the two bodies.

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