The temperature of 20 litres of nitrogen was increased from 100 K to 300 K at a constant pressure. Change in volume will be

Options

A. 80 litre
B. 60 litre
C. 40 litre
D. 20 litre

Explanation

To solve the problem of finding the change in volume of nitrogen gas when its temperature is increased from 100 K to 300 K at constant pressure, we can use the ideal gas law and the relationship between volume and temperature.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Initial volume (V1) = 20 liters
- Initial temperature (T1) = 100 K
- Final temperature (T2) = 300 K

2. **Use the Direct Relationship Between Volume and Temperature:**
According to Charles's Law, at constant pressure, the volume of a gas is directly proportional to its absolute temperature. This can be expressed as:
\[ \frac{V1}{T1} = \frac{V2}{T2} \]
where V2 is the final volume we need to find.

3. **Substitute the Known Values into the Equation:**
\[ \frac{20 \, \text{liters}}{100 \, \text{K}} = \frac{V2}{300 \, \text{K}} \]

4. **Cross-Multiply to Solve for V2:**
\[ 20 \, \text{liters} \times 300 \, \text{K} = V2 \times 100 \, \text{K} \]
\[ 6000 = 100 \, V2 \]

5. **Calculate V2:**
\[ V2 = \frac{6000}{100} = 60 \, \text{liters} \]

6. **Determine the Change in Volume:**
The change in volume (ΔV) is calculated as:
\[ \Delta V = V2 - V1 \]
\[ \Delta V = 60 \, \text{liters} - 20 \, \text{liters} = 40 \, \text{liters} \]

### Final Answer:
The change in volume is **40 liters**.

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