Discussion
For an ideal gas with constant properties undergoing a quasi-static process, which one of the following represents the change of entropy (Δs) from state 1 to 2?
Answer: A
The correct expression is \(\Delta s = C_{p}\ln\frac{T_{2}}{T_{1}} - R\ln\frac{P_{2}}{P_{1}}\).
From the Gibbs relation \(T\,ds = dh - v\,dP\), with \(dh = C_{p}\,dT\) and \(v = RT/P\) for an ideal gas:
\[ \begin{aligned} ds &= C_{p}\frac{dT}{T} - R\frac{dP}{P} \\ \Delta s &= C_{p}\ln\frac{T_{2}}{T_{1}} - R\ln\frac{P_{2}}{P_{1}} \end{aligned} \]
The volume form is \(\Delta s = C_{V}\ln\frac{T_{2}}{T_{1}} + R\ln\frac{V_{2}}{V_{1}}\). Option D has \(R\ln(V_{1}/V_{2})\), which reverses the sign of the volume term. Options B and C put a heat capacity where R belongs.
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