Question

100 calories of heat is given to a gas in a vessel fitted with a movable piston. The gas does 40 joules of work in expansion. The increase in internal energy is

• A. 578 J
• B. 478 J
• C. 318 J
• D. 218 J

Hint:

The first law of thermodynamics ties heat, work, and internal energy. When heat is in calories, always convert to joules using 1, calorie = 4.184,J. This is especially useful in thermodynamic problems involving energy balance.

Answer 1

The Correct Option is C

From the first law of thermodynamics:
\[\Delta U = Q - W\]
Given \(Q = 100 \, \text{calories} = 100 \times 4.184 \, \text{J} = 418.4 \, \text{J}\) and \(W = 40 \, \text{J}\):
\[\Delta U = 418.4 - 40 \approx 318 \, \text{J}\]