Among the following the correct statement is

Options

A. Internal energy of a gas depends only on the state of the gas.
B. In an isothermal process change in internal energy in maximum
C. Area under pressure, volume graph equals heat supplied in any process.
D. Work done is state dependent but not path dependent.

Answer

To solve the question regarding the correct statement about thermodynamics, we will analyze each of the provided statements step by step.

### Step 1: Analyze the First Statement
**Statement:** Internal energy of gas depends only on the state of the gas.

**Explanation:**
- The internal energy of a gas is a function of its state variables, such as temperature, volume, and number of particles.
- It does not depend on the path taken to reach that state.
- Therefore, this statement is **correct**.

### Step 2: Analyze the Second Statement
**Statement:** In an isothermal process, change in internal energy is maximum.

**Explanation:**
- In an isothermal process, the temperature remains constant, which means the change in temperature (ΔT) is zero.
- The formula for change in internal energy (ΔU) is given by ΔU = nCvΔT. Since ΔT = 0, ΔU = 0.
- Therefore, the change in internal energy is not maximum; in fact, it is zero. This statement is **incorrect**.

### Step 3: Analyze the Third Statement
**Statement:** Area under the pressure-volume graph equals heat supplied in any process.

**Explanation:**
- The area under the pressure-volume (P-V) graph represents the work done by or on the gas, not the heat supplied.
- Therefore, this statement is **incorrect**.

### Step 4: Analyze the Fourth Statement
**Statement:** Work done is state dependent but not path dependent.

**Explanation:**
- Work done in a thermodynamic process depends on the path taken between the initial and final states.
- Different paths can yield different amounts of work done, even if the initial and final states are the same.
- Hence, this statement is **incorrect**.

### Conclusion
After analyzing all the statements, we find that the only correct statement is:

**Correct Statement:** Internal energy of gas depends only on the state of the gas.