The work done by expansion at constant temperature To of a particular system from a V volume Vo to a volume V is given by W = NkT, In. Vo We also know that, for this system, its entropy is : S= N k- Vo (T V. To 1. Calculate the Helmholtz free energy F of the system. 2. Determine the equation of state of the system. 3. Calculate the work done at an arbitrary temperature T by an expansion from volume V, to volume V.

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The work done by expansion at constant temperature To of a particular system from a
V
volume Vo to a volume V is given by W = NkT, In
Vo
We also know that, for this system, its entropy is : S = Nk-
Vo (T
V To
1. Calculate the Helmholtz free energy F of the system.
2. Determine the equation of state of the system.
3. Calculate the work done at an arbitrary temperature T by an expansion from volume
Vo to volume V.
Transcribed Image Text:The work done by expansion at constant temperature To of a particular system from a V volume Vo to a volume V is given by W = NkT, In Vo We also know that, for this system, its entropy is : S = Nk- Vo (T V To 1. Calculate the Helmholtz free energy F of the system. 2. Determine the equation of state of the system. 3. Calculate the work done at an arbitrary temperature T by an expansion from volume Vo to volume V.
Expert Solution
Step 1

In the given system, the temperature is constant, the process is isothermal.

The Helmholtz free energy F is given by

F=U-TS........1Differentiating 1 dF=dU-TdS-SdT......2From first law of thermodynamicsdQ=dU+dWdU=dQ-dW.....3Using 3 in 2dF=dQ-dW-TdS-SdTdF=TdS-dW-TdS-SdT   SdT=0 for constant temperature processdF=-dWF=-W

The Helmholtz free energy is 

F=-W=-NkTolnVVo=NkTolnVoVF=NkTolnVoV      

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