Discussion
The equation of state for a non-ideal gas is
\[ \frac{Pv}{RT} = 1 + BP \]
where \(P\) is pressure, \(v\) is specific volume, \(R\) is the specific gas constant, \(T\) is temperature, and \(B\) is a temperature dependent parameter. For this gas, the partial derivative of enthalpy with respect to pressure at constant temperature is
Answer: B
The derivative is \(-RT^{2}\left(\frac{dB}{dT}\right)\).
The general relation is \((\partial h/\partial P)_T = v - T(\partial v/\partial T)_P\). From the equation of state, \(v = RT/P + BRT\), so
\[ \begin{aligned} \left(\frac{\partial v}{\partial T}\right)_P &= \frac{R}{P} + BR + RT\frac{dB}{dT} \\ v - T\left(\frac{\partial v}{\partial T}\right)_P &= -RT^{2}\frac{dB}{dT} \end{aligned} \]
The ideal-gas part \(RT/P\) and the \(BRT\) term both cancel. BRT is what remains if B is treated as constant in only one of the two terms, and 0 is the ideal-gas result, which holds here only if B does not depend on T.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development