In an isothermal expansion of one mole of an ideal gas against vacuum from 10 litre to 100 litre at `27^(@)C`, the quantity of heat absorbed by the gas is

Answer

To solve the problem of the quantity of heat absorbed by the gas during an isothermal expansion against vacuum, we can follow these steps:

### Step-by-step Solution:

1. **Understand the Process**:
- We have an isothermal expansion of one mole of an ideal gas.
- The gas expands from a volume of 10 liters to 100 liters at a constant temperature of 27 °C.

2. **Identify Key Concepts**:
- **Isothermal Process**: In an isothermal process, the temperature (T) remains constant. Therefore, the change in internal energy (ΔU) for an ideal gas is zero because ΔU = nCvΔT, and ΔT = 0.
- **First Law of Thermodynamics**: The first law states that ΔU = Q + W, where Q is the heat absorbed, and W is the work done by the system.

3. **Calculate Change in Internal Energy (ΔU)**:
- Since the process is isothermal for an ideal gas, ΔU = 0.

4. **Apply the First Law of Thermodynamics**:
- From the first law, we have:
\[ ΔU = Q + W \]
- Substituting ΔU = 0:
\[ 0 = Q + W \]
- Rearranging gives:
\[ Q = -W \]

5. **Determine Work Done (W)**:
- Since the gas is expanding against a vacuum, the external pressure (P_ext) is zero. Thus, the work done by the gas is:
\[ W = -P_{ext} \Delta V = -0 \times (V_f - V_i) = 0 \]
- Therefore, W = 0.

6. **Calculate Heat Absorbed (Q)**:
- Substituting W = 0 into the equation for Q:
\[ Q = -W = -0 = 0 \]

### Final Answer:
The quantity of heat absorbed by the gas during the isothermal expansion is **0 Joules**.