Given below are two statements:
Statement I: If heat is added to a system, its temperature must increase.
Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase.
In the light of the above statements, choose the correct answer from the options given below

Solution

Physics sir · 4 steps

Heat can go into doing work instead of warming the gas. Work by a gas, though, always needs it to expand.

1. First law. Heat given to a system splits into two parts: some raises its internal energy, and the rest goes out as work done by the system.

   Δ Q = Δ U + W

2. Statement I. In an isothermal expansion of an ideal gas, Δ T = 0, so Δ U = 0 and all the heat added becomes work, Δ Q = W. Heat goes in and the temperature does not rise. During melting or boiling too, heat is absorbed at constant temperature. So Statement I is false.
3. Statement II. Work done by a system is W = ∫ P dV. Pressure is always positive, so W has the same sign as the change in volume dV. Positive work therefore means dV > 0, that is, the volume increases. So Statement II is true.
4. So. Statement I is false and Statement II is true, which is option (b).

The idea to keep. Heat added does not have to raise temperature. It can all leave as work, as in isothermal expansion or a phase change. The sign of work done by a gas follows the sign of dV, because pressure is always positive.

Answer from the NTA final answer key. Solution by PrepWiser.