1 g of a liquid is converted to vapour at 3 × 10⁵ Pa pressure. If 10% of the heat supplied is used for increasing the volume by 1600 cm³ during this phase change, then the increase in internal energy in the process will be :

Solution

Physics sir · 4 steps

Find the work from PΔ V first. It is only 10% of the heat, and the remaining 90% goes into U.

1. Work by expansion. The vapour pushes out at constant pressure, so W = PΔ V. Convert the volume first: 1600 cm³ = 1600 × 10⁻⁶ m³ = 1.6 × 10⁻³ m³.

   W = PΔ V = (3 × 10⁵) × (1.6 × 10⁻³) = 480 J

2. Total heat. This 480 J is 10% of the heat supplied, so Q = 480/0.1 = 4800 J.
3. First law. Δ U = Q - W = 4800 - 480 = 4320 J. This is the 90% of the heat that was not used for expansion.
4. So. The internal energy increases by 4320 J, which is option (b).

The idea to keep. In a phase change, the heat splits two ways: PΔ V pushes the surroundings back, and the rest raises internal energy. Always convert cm³ to m³ with 10⁻⁶.

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