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GATE 2025 AE – Question 31

Propulsion · Basics of thermodynamics · 1 mark · Multiple choice

$\delta Q$ and $\delta W$ are the heat and work interactions of a system with its surroundings, and $dU$ is the change in the internal energy of the system. For an adiabatic process in a closed, constant pressure combustor, which one of the following options is correct?

  1. $|\delta Q| = |dU| \neq 0$ and $|\delta W| = 0$
  2. $|\delta Q| = |\delta W| = 0$ and $|dU| \neq 0$
  3. $|\delta Q| = |\delta W| = |dU| = 0$
  4. $|\delta W| = |dU| \neq 0$ and $|\delta Q| = 0$

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Correct answer: (D) $|\delta W| = |dU| \neq 0$ and $|\delta Q| = 0$

Explanation

The process is adiabatic, so $\delta Q = 0$. Combustion at constant pressure in a closed system makes the gas expand, so it does boundary work $\delta W = p\,dV \ne 0$. The first law gives $dU = \delta Q - \delta W = -\delta W$, so $|\delta W| = |dU| \ne 0$.