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

Options

A. (A) 163.7 cal
B. (B) zero
C. (C) 1381.1 cal
D. (D) 9 L atm

Explanation

To solve the problem step by step, we will analyze the situation involving the isothermal expansion of an ideal gas.

### Step 1: Understand the process
We are given that 1 mole of an ideal gas is expanded isothermally from an initial volume of 1 liter to a final volume of 10 liters at a constant temperature of 300 K.

### Step 2: Recall the properties of an ideal gas
For an ideal gas, the internal energy (U) is a function of temperature only. Therefore, for an ideal gas, the change in internal energy (ΔE) during an isothermal process (where temperature remains constant) is given by:

\[ \Delta E = n C_V \Delta T \]

where:
- \( n \) = number of moles
- \( C_V \) = molar heat capacity at constant volume
- \( \Delta T \) = change in temperature

### Step 3: Analyze the isothermal condition
In an isothermal process, the temperature does not change. Hence, the change in temperature (ΔT) is zero:

\[ \Delta T = T_{\text{final}} - T_{\text{initial}} = 300 K - 300 K = 0 \]

### Step 4: Substitute into the equation
Since ΔT = 0, we can substitute this into the equation for ΔE:

\[ \Delta E = n C_V \cdot 0 = 0 \]

### Step 5: Conclusion
Thus, the change in internal energy (ΔE) for the isothermal expansion of the ideal gas is:

\[ \Delta E = 0 \]

The correct answer is option B: 0.

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