The temperature of 20 L of nitrogen was increased from 10 K to 30 K at a constant pressure. Change in volume will be

Options

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

Answer

To solve the problem of finding the change in volume of nitrogen gas when its temperature is increased from 10 K to 30 K at constant pressure, we can use the ideal gas law and the relationship between volume and temperature.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Initial Volume (V1) = 20 L
- Initial Temperature (T1) = 10 K
- Final Temperature (T2) = 30 K

2. **Use the Ideal Gas Law Relationship:**
- At constant pressure, the volume of a gas is directly proportional to its temperature (in Kelvin).
- This can be expressed as:
\[ \frac{V1}{T1} = \frac{V2}{T2} \]

3. **Rearranging the Formula:**
- To find the final volume (V2), we can rearrange the equation:
\[ V2 = V1 \times \frac{T2}{T1} \]

4. **Substituting the Values:**
- Now substitute the known values into the equation:
\[ V2 = 20 \, \text{L} \times \frac{30 \, \text{K}}{10 \, \text{K}} \]

5. **Calculating V2:**
- Simplifying the equation:
\[ V2 = 20 \, \text{L} \times 3 = 60 \, \text{L} \]

6. **Finding the Change in Volume:**
- The change in volume (ΔV) can be calculated as:
\[ \Delta V = V2 - V1 \]
- Substituting the values:
\[ \Delta V = 60 \, \text{L} - 20 \, \text{L} = 40 \, \text{L} \]

7. **Final Answer:**
- The change in volume is **40 L**.