An ideal gas receives 10J of heat in a reversible isothermal expansion. Then the work done by the gas:

Options

A. Would be more than 10 J
B. 10J
C. Would be less than 10 J
D. Cannot be determined

Explanation

To solve the problem of finding the work done by an ideal gas during a reversible isothermal expansion when it receives 10 J of heat, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Process**:
- The process is isothermal, which means the temperature of the gas remains constant throughout the expansion. Therefore, the change in internal energy (ΔU) of the gas is zero.

2. **Apply the First Law of Thermodynamics**:
- The first law of thermodynamics is given by the equation:
\[ \Delta U = Q + W \]
- Where:
- ΔU = Change in internal energy
- Q = Heat added to the system
- W = Work done by the system

3. **Substitute Known Values**:
- Since the process is isothermal, we have:
\[ \Delta U = 0 \]
- The heat added to the system (Q) is given as 10 J. Therefore, we can substitute these values into the equation:
\[ 0 = 10 J + W \]

4. **Rearrange the Equation**:
- To find the work done (W), we rearrange the equation:
\[ W = -10 J \]

5. **Interpret the Result**:
- The negative sign indicates that the work is done by the gas on the surroundings during the expansion. Therefore, the work done by the gas is 10 J.

### Final Answer:
The work done by the gas during the reversible isothermal expansion is **10 J**.

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