In an isothermal process for an ideal gas

Options

A. `DeltaQ =0`
B. `DeltaW = 0`
C. `DeltaU = 0`
D. `DeltaV = 0`

Answer

To solve the question regarding the isothermal process for an ideal gas, let's break down the concepts step by step.

### Step-by-Step Solution:

1. **Understanding Isothermal Process**:
- An isothermal process is one in which the temperature (T) of the system remains constant throughout the process. For an ideal gas, this implies that the internal energy (U) of the gas does not change since internal energy is a function of temperature.

**Hint**: Remember that in an isothermal process, temperature remains constant.

2. **Change in Internal Energy (ΔU)**:
- For an ideal gas, the change in internal energy (ΔU) is given by the formula:
\[ \Delta U = mC_v \Delta T \]
where \(C_v\) is the specific heat at constant volume, and \(m\) is the mass of the gas. Since the temperature does not change (ΔT = 0), we have:
\[ \Delta U = mC_v \cdot 0 = 0 \]

**Hint**: Recall that for an ideal gas, internal energy depends solely on temperature.

3. **First Law of Thermodynamics**:
- The first law of thermodynamics states:
\[ \Delta Q = \Delta W + \Delta U \]
Substituting ΔU = 0 into this equation gives:
\[ \Delta Q = \Delta W + 0 \implies \Delta Q = \Delta W \]

**Hint**: The first law of thermodynamics relates heat transfer, work done, and change in internal energy.

4. **Work Done (ΔW)**:
- In an isothermal process, the gas does work on the surroundings as it expands or is compressed. Therefore, the work done (ΔW) is not zero. Since ΔQ = ΔW, it follows that ΔQ is also not zero.

**Hint**: In an isothermal process, the gas can do work, which means ΔW cannot be zero.

5. **Conclusion**:
- From the above analysis, we conclude:
- ΔU = 0 (no change in internal energy)
- ΔW ≠ 0 (work is done)
- ΔQ = ΔW (heat added equals work done)

Therefore, the correct option is that the change in internal energy (ΔU) is zero.

### Final Answer:
The correct answer is that the change in internal energy (ΔU) for an ideal gas in an isothermal process is zero.