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Derive expressions for (a) Δu, (b) Δh, and (c) Δs for a gas whose equation of state is P(v − a) = RT for an isothermal process.
(a)

To drive an expression of
Answer to Problem 42P
The expression of
Explanation of Solution
Write the equation of state of the given gas.
Here, the temperature is
Write the general expression for change in internal energy
Here, the internal energy at state 1, 2 is
Rearrange the Equation (I) to obtain
Conclusion:
Partially differentiate the Equation (III) with respect to temperature by keeping the specific volume as constant.
Substitute
For an isothermal process, the temperature is kept constant.
The differential temperature or change in temperature becomes zero.
Substitute
Thus, the expression of
(b)

To drive an expression of
Answer to Problem 42P
The expression of
Explanation of Solution
Write the general expression for change in enthalpy
Here, the enthalpy at state 1, 2 is
Rearrange the Equation (V) to obtain
Conclusion:
Partially differentiate the Equation (VI) with respect to temperature by keeping the pressure as constant.
Substitute
For an isothermal process, the temperature is kept constant.
The differential temperature or change in temperature becomes zero.
Substitute
Thus, the expression of
(c)

To drive an expression of
Answer to Problem 42P
The expression of
Explanation of Solution
Write the general expression for change in entropy
Here, the entropy at state 1, 2 is
Conclusion:
Substitute
For an isothermal process, the temperature is kept constant.
The differential temperature or change in temperature becomes zero.
Substitute
Thus, the expression of
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Chapter 12 Solutions
Thermodynamics: An Engineering Approach ( 9th International Edition ) ISBN:9781260092684
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