Heat is given to an ideal gas in an isothermal process.
A. Internal energy of the gas will decrease.
B. Internal energy of the gas will increase.
C. Internal energy of the gas will not change.
D. The gas will do positive work.
E. The gas will do negative work.
Choose the correct answer from the options given below :

Solution

Physics sir · 4 steps

Isothermal means T is fixed, so U is fixed too. Every joule of heat you give goes out as work.

1. Internal energy. For an ideal gas, internal energy depends only on temperature. In an isothermal process T does not change, so Δ U = 0. That makes statement C true, and A and B false.
2. First law. Use the first law with W as the work done by the gas.

   Q = Δ U + W ⇒ W = Q - 0 = Q

3. Sign of work. Heat is given to the gas, so Q > 0, and therefore W > 0. The gas expands and does positive work. Statement D is true and E is false.
4. So. Only C and D are correct, which is option (d).

The idea to keep. For an ideal gas, U depends on T alone. Isothermal gives Δ U = 0, so Q = W: heat in means positive work by the gas, heat out means work done on it.

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