JEE Main 2023 · 31 January · morning · Single correct · +4 / −1
The pressure of a gas changes linearly with volume from A to B as shown in figure. If no heat is supplied to or extracted from the gas then change in the internal energy of the gas will be
- (a) 6 J
- (b) 4.5 J
- (c) zero
- (d) -4.5 J
Answer and solution
Answer (b) 4.5 J
Solution
Physics sir · 4 steps
No heat flows, so all the work done on the gas goes into it: find the area under the line.
- Work from the graph. The work done by the gas is the area under the P–V line. From A to B the volume falls from 200 cc to 50 cc, so the gas is compressed and this work is negative.
|W| = 1/2(10 + 50) × 10³ Pa × (200 - 50) × 10⁻⁶ m³ = 4.5 J
- Sign of work. The area is a trapezium with parallel sides 10 kPa and 50 kPa and width 150 cc. Since this is a compression, the work done by the gas is W = -4.5 J.
- First law. With Q = 0, Δ U = Q - W = 0 - (-4.5 J) = +4.5 J.
- So. The internal energy of the gas increases by 4.5 J, which is option (b).
The idea to keep. If no heat flows, the change in internal energy is minus the work done by the gas. A compression means work is done on the gas, so its internal energy goes up.
Answer from the NTA final answer key. Solution by PrepWiser.