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GATE 2017 ME (ME2) – Question 24

Thermodynamics · Ideal and real gases · 1 mark · Multiple choice

Mass m of a perfect gas undergoes an isothermal process from pressure p₁, volume V₁ to pressure p₂, volume V₂. Work on the system is positive. For gas constant R and temperature T, the work is ______.

  1. $p_1V_1\ln(V_2/V_1)$
  2. $-p_1V_1\ln(p_1/p_2)$
  3. $RT\ln(V_2/V_1)$
  4. $-mRT\ln(p_2/p_1)$

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Correct answer: (B) $-p_1V_1\ln(p_1/p_2)$

Explanation

For a quasistatic ideal-gas isothermal path, work by the gas is ∫p dV=mRT ln(V2/V1). Work on the gas is its negative: −p1V1 ln(V2/V1). Since V2/V1=p1/p2, this is **−p1V1 ln(p1/p2), B**. Compression then gives positive work on the system.