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 Charles's Law. Here’s a step-by-step solution:

### Step 1: Understand Charles's Law
Charles's Law states that at constant pressure, the volume of a gas is directly proportional to its absolute temperature. Mathematically, it can be expressed as:
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
where:
- \( V_1 \) = initial volume
- \( T_1 \) = initial temperature
- \( V_2 \) = final volume
- \( T_2 \) = final temperature

### Step 2: Identify the Given Values
From the problem, we have:
- \( V_1 = 20 \) liters
- \( T_1 = 100 \) K
- \( T_2 = 300 \) K

### Step 3: Substitute the Values into Charles's Law
We can substitute the known values into the equation:
\[ \frac{20}{100} = \frac{V_2}{300} \]

### Step 4: Solve for \( V_2 \)
Cross-multiply to solve for \( V_2 \):
\[ 20 \times 300 = 100 \times V_2 \]
\[ 6000 = 100 V_2 \]
Now, divide both sides by 100:
\[ V_2 = \frac{6000}{100} = 60 \text{ liters} \]

### Step 5: Calculate the Change in Volume
The change in volume (\( \Delta V \)) is calculated as:
\[ \Delta V = V_2 - V_1 \]
Substituting the values we found:
\[ \Delta V = 60 \text{ liters} - 20 \text{ liters} = 40 \text{ liters} \]

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

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