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GATE 2019 ME (ME2) – Question 22

Thermodynamics · Thermodynamic relations and property charts · 1 mark · Multiple choice

For a simple compressible system with specific volume v, specific entropy s, pressure p and temperature T, which equals $(\partial v/\partial s)_p$ by Maxwell’s relations?

  1. $(\partial s/\partial T)_v$
  2. $(\partial p/\partial v)_T$
  3. $-(\partial T/\partial v)_p$
  4. $(\partial T/\partial p)_s$

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Show answer and explanation

Correct answer: (D) $(\partial T/\partial p)_s$

Explanation

Enthalpy differential is $dh=T\,ds+v\,dp$. Equality of mixed derivatives gives $(\partial v/\partial s)_p=(\partial T/\partial p)_s$. **D**.