Calculate work done during isothermal reversible process when
`5 mol` ideal gas is expanded so that its volume is doubled at `400K`.

Options

A. `-11.5 kJ`
B. `- 344 kJ`
C. 0
D. `-2.8 kJ`

Explanation

To calculate the work done during an isothermal reversible process when 5 moles of an ideal gas are expanded so that its volume is doubled at 400 K, we can follow these steps:

### Step 1: Identify the given values
- Number of moles (n) = 5 mol
- Initial temperature (T) = 400 K
- Initial volume (V1) = V (let's assume the initial volume is V)
- Final volume (V2) = 2V (since the volume is doubled)

### Step 2: Use the formula for work done in an isothermal reversible process
The work done (W) during an isothermal reversible expansion can be calculated using the formula:
\[ W = -2.303 \, nRT \log \left( \frac{V_2}{V_1} \right) \]

### Step 3: Substitute the known values into the formula
- The universal gas constant (R) = 8.314 J/(mol·K)
- Substitute n, R, T, V2, and V1 into the formula:
\[ W = -2.303 \times 5 \, \text{mol} \times 8.314 \, \text{J/(mol·K)} \times 400 \, \text{K} \log \left( \frac{2V}{V} \right) \]

### Step 4: Simplify the logarithm
Since \( \frac{V_2}{V_1} = \frac{2V}{V} = 2 \):
\[ \log(2) \approx 0.301 \]

### Step 5: Substitute the logarithm value into the equation
\[ W = -2.303 \times 5 \times 8.314 \times 400 \times 0.301 \]

### Step 6: Calculate the work done
Now, calculate the numerical value:
1. Calculate \( 2.303 \times 5 = 11.515 \)
2. Calculate \( 11.515 \times 8.314 \approx 95.75 \)
3. Calculate \( 95.75 \times 400 = 38300 \)
4. Finally, calculate \( 38300 \times 0.301 \approx 11550.3 \)

Since the work done is negative (as it is work done by the system), we have:
\[ W \approx -11550.3 \, \text{J} \]

### Step 7: Convert to kilojoules
To convert joules to kilojoules, divide by 1000:
\[ W \approx -11.55 \, \text{kJ} \]

### Final Answer
The work done during the isothermal reversible process is approximately:
\[ W \approx -11.55 \, \text{kJ} \]