One mole of an ideal gas at 300 K is expanded isothermally from an initial volume of 1 L to 10 L. The `DeltaE` for this process is (R=2 cal . `"mol"^(-1)K^(-1)`)

Options

A. 163.7cal
B. zero
C. 1381.1cal
D. 9lit. Atm

Explanation

To solve the problem of finding the change in internal energy (ΔE) for one mole of an ideal gas undergoing isothermal expansion, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Process**: The gas is expanding isothermally, meaning that the temperature remains constant throughout the process. For an ideal gas, the internal energy (U) is a function of temperature only.

2. **Identify Given Values**:
- Number of moles (n) = 1 mole
- Initial volume (V1) = 1 L
- Final volume (V2) = 10 L
- Temperature (T) = 300 K
- Gas constant (R) = 2 cal/(mol·K)

3. **Recall the Internal Energy Change Formula**: For an ideal gas, the change in internal energy (ΔE) during an isothermal process is given by:
\[ \Delta E = n C_V \Delta T \]
where \(C_V\) is the molar specific heat capacity at constant volume and \(\Delta T\) is the change in temperature.

4. **Determine ΔT**: Since the process is isothermal, the temperature does not change:
\[ \Delta T = T_{final} - T_{initial} = 300 K - 300 K = 0 K \]

5. **Substitute into the Formula**: Now substitute the values into the internal energy change formula:
\[ \Delta E = n C_V \Delta T = 1 \text{ mol} \cdot C_V \cdot 0 = 0 \]

6. **Conclusion**: The change in internal energy (ΔE) for the isothermal expansion of one mole of an ideal gas is:
\[ \Delta E = 0 \text{ cal} \]

### Final Answer:
\[ \Delta E = 0 \text{ cal} \]