To calculate the amount of work done in joules during reversible isothermal expansion of an ideal gas, the volume must be expressed in

Options

A. `m^(3)` only
B. `dm^(3)` only
C. `cm^(3)` only
D. Any one of them

Explanation

To calculate the amount of work done during the reversible isothermal expansion of an ideal gas, we need to follow these steps:

### Step 1: Understand the Work Done Formula
The work done (W) during the expansion of an ideal gas can be expressed using the formula:
\[ W = P \Delta V \]
where:
- \( W \) = work done
- \( P \) = pressure
- \( \Delta V \) = change in volume

### Step 2: Identify the Units of Volume
In the formula, the volume change (\( \Delta V \)) can be expressed in various units. Commonly, volume is expressed in:
- liters (L)
- cubic meters (m³)
- cubic centimeters (cm³)

### Step 3: Convert Units to Joules
When using the formula \( W = P \Delta V \), if pressure is in atmospheres (atm) and volume is in liters (L), the work done will be in the unit of atm·L. To convert this to joules, we use the conversion factor:
\[ 1 \text{ atm·L} = 101.3 \text{ joules} \]

### Step 4: Choose the Volume Unit
For the calculation, you can express the volume in any unit, such as:
- Liters (L)
- Cubic meters (m³)
- Cubic centimeters (cm³)

However, if you choose to express volume in liters, remember to convert the final result from atm·L to joules using the conversion factor mentioned above.

### Conclusion
To summarize, the volume must be expressed in a unit that can be converted to joules, such as liters, cubic meters, or cubic centimeters. The correct answer is that the volume can be expressed in any of these units, but it is essential to convert the final work done into joules.