Question

The heat supplied to a gas at a constant pressure of $5 \times 10^5\, Pa$ is 1000 kJ. If the volume of gas changes from 1 m$^3$ to 2.5 m$^3$, then the change in internal energy of the gas is

• A. 250 kJ
• B. 225 kJ
• C. 200 kJ
• D. 175 kJ

Hint:

Use the first law of thermodynamics: \(\Delta U = Q - W\), where work done by the gas is pressure times change in volume.

Answer 1

The Correct Option is A

Given: Pressure \(P = 5 \times 10^5\, Pa\), heat supplied \(Q = 1000\, kJ\)
Volume change \(\Delta V = 2.5 - 1 = 1.5\, m^3\)
Work done by gas: \[ W = P \Delta V = 5 \times 10^5 \times 1.5 = 7.5 \times 10^5\, J = 750\, kJ \] Change in internal energy: \[ \Delta U = Q - W = 1000 - 750 = 250\, kJ \]