For an isothermal reversible expansion process, the value of q can be calculated by the expressin

Options

A. `q=2.303 n RT log. (V_(2))/(V_(1))`
B. `q=-2.303nRT log.(V_(2))/(V_(1))`
C. `q=-2.303 nRT log. (V_(1))/(V_(2))`
D. `q=-P_("exp")nRT log.(V_(1))/(V_(2))`

Explanation

To solve the problem regarding the calculation of \( q \) for an isothermal reversible expansion process, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Isothermal Process**:
- An isothermal process is one where the temperature (\( T \)) of the system remains constant throughout the process. Therefore, the change in temperature (\( \Delta T \)) is equal to 0.

2. **Apply the First Law of Thermodynamics**:
- The first law of thermodynamics states that:
\[ \Delta U = Q + W \]
- Where \( \Delta U \) is the change in internal energy, \( Q \) is the heat added to the system, and \( W \) is the work done by the system.

3. **Determine Change in Internal Energy**:
- For an ideal gas, the change in internal energy (\( \Delta U \)) can be expressed as:
\[ \Delta U = n C_V \Delta T \]
- Since \( \Delta T = 0 \) for an isothermal process, it follows that:
\[ \Delta U = 0 \]

4. **Relate Heat and Work**:
- From the first law of thermodynamics, substituting \( \Delta U = 0 \):
\[ 0 = Q + W \implies Q = -W \]

5. **Calculate Work Done (W)**:
- The work done during an isothermal expansion of an ideal gas can be calculated using the formula:
\[ W = -nRT \ln\left(\frac{V_2}{V_1}\right) \]
- Here, \( n \) is the number of moles, \( R \) is the universal gas constant, \( T \) is the absolute temperature, \( V_2 \) is the final volume, and \( V_1 \) is the initial volume.

6. **Substitute Work into the Heat Equation**:
- Now substituting the expression for \( W \) into the equation for \( Q \):
\[ Q = -(-nRT \ln\left(\frac{V_2}{V_1}\right)) = nRT \ln\left(\frac{V_2}{V_1}\right) \]

7. **Final Expression for Q**:
- Thus, we can express \( Q \) as:
\[ Q = nRT \ln\left(\frac{V_2}{V_1}\right) \]

8. **Check Options**:
- Finally, check the provided options to find the one that matches this derived expression for \( Q \).