The work done to contract a gas in a cylinder is 462 joules. 128 joule energy is evolved in the process. What

Question

The work done to contract a gas in a cylinder is 462 joules. 128 joule energy is evolved in the process. What will be the internal energy change in the process? [MP PMT 2003]

Accepted Answer

To determine the change in internal energy ($\Delta U$), we apply the **First Law of Thermodynamics**, which is mathematically expressed as $\Delta U = q + w$ .

1.  **Work ($w$):** According to the IUPAC sign convention used in thermodynamics, work done **on the system** (such as during compression or contraction) is assigned a **positive sign** . Therefore, $w = +462$ J.
2.  **Heat ($q$):** Heat **evolved** (released) by the system to the surroundings is assigned a **negative sign** . Therefore, $q = -128$ J.
3.  **Calculation:** Substituting these values into the first law equation:
    $\Delta U = (-128	ext{ J}) + (+462	ext{ J}) = +334	ext{ J}$.

The internal energy of the system increases by **334 joules**, which matches Option C.

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