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:

We need to identify the correct statements about heat given to an ideal gas in an isothermal process.

In an isothermal process:

Temperature remains constant, i.e., $$\Delta T = 0$$.

Statement A: Internal energy will decrease.

For an ideal gas, internal energy depends only on temperature: $$U = nC_vT$$. Since $$\Delta T = 0$$, we have $$\Delta U = 0$$. Statement A is INCORRECT.

Statement B: Internal energy will increase.

Since $$\Delta U = 0$$, Statement B is INCORRECT.

Statement C: Internal energy will not change.

Since $$\Delta U = 0$$, Statement C is CORRECT. ✓

Statement D: The gas will do positive work.

By first law: $$Q = \Delta U + W$$. Since $$\Delta U = 0$$ and $$Q > 0$$ (heat is given), we get $$W = Q > 0$$.

The gas does positive work (it expands). Statement D is CORRECT. ✓

Statement E: The gas will do negative work.

Since $$W > 0$$, Statement E is INCORRECT.

The correct answer is Option 4: C and D only.