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, we will use the direct relationship between volume and temperature at constant pressure, which is given by Charles's Law. According to Charles's Law, the volume of a gas is directly proportional to its absolute temperature when pressure is held constant.

### Step-by-step Solution:

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

2. **Use Charles's Law:**
Charles's Law states that:
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
Where:
- \( V_1 \) = initial volume
- \( T_1 \) = initial temperature
- \( V_2 \) = final volume
- \( T_2 \) = final temperature

3. **Substitute Known Values:**
Plugging in the known values into the equation:
\[ \frac{20 \, \text{L}}{10 \, \text{K}} = \frac{V_2}{30 \, \text{K}} \]

4. **Cross-Multiply to Solve for \( V_2 \):**
\[ 20 \, \text{L} \times 30 \, \text{K} = V_2 \times 10 \, \text{K} \]
\[ 600 = 10 V_2 \]
\[ V_2 = \frac{600}{10} = 60 \, \text{L} \]

5. **Calculate the Change in Volume:**
The change in volume (\( \Delta V \)) can be calculated as:
\[ \Delta V = V_2 - V_1 \]
\[ \Delta V = 60 \, \text{L} - 20 \, \text{L} = 40 \, \text{L} \]

6. **Conclusion:**
The change in volume is 40 L.

### Final Answer:
The change in volume will be **40 L**.