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Thermodynamics
Entropy & Second Law
GATE 2008
Medium

In a steady state steady flow process with a single inlet and single outlet, the work done per unit mass flow rate is w=-∫(inlet to outlet) v dp, where v is specific volume and p is pressure. This expression for w

  • Ais valid only if the process is both reversible and adiabatic
  • Bis valid only if the process is both reversible and isothermal
  • is valid for any reversible process
  • Dis incorrect; it must be w=∫(inlet to outlet) p dv

Explanation

For any reversible process, Tds=dh-vdp (Gibbs relation), so -∫vdp=-∫dh+∫Tds=-Δh+q_rev. Combined with the steady-flow energy balance w=q-Δh, this gives w=-∫vdp for ANY reversible steady-flow process (not restricted to adiabatic or isothermal).

Source: GATE ME 2008 (2008)

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