One litre of an ideal gas st `27^(@)C` is heated at a constant pressure to the `297^(@)C.` Then, the final volume is the approximately

Options

A. 1.2 L
B. 1.9 L
C. 19 L
D. 2.4 L

Explanation

To solve the problem of finding the final volume of an ideal gas when heated at constant pressure, we can use the relationship between volume and temperature for an ideal gas. Here’s a step-by-step solution:

### Step 1: Understand the relationship between volume and temperature
For an ideal gas at constant pressure, the volume (V) is directly proportional to the absolute temperature (T). This can be expressed as:
\[ V \propto T \]

### Step 2: Convert temperatures from Celsius to Kelvin
We need to convert the given temperatures from degrees Celsius to Kelvin:
- Initial temperature \( T_1 = 27^\circ C = 27 + 273 = 300 \, K \)
- Final temperature \( T_2 = 297^\circ C = 297 + 273 = 570 \, K \)

### Step 3: Write the ratio of volumes and temperatures
Using the proportionality established earlier, we can write:
\[ \frac{V_2}{V_1} = \frac{T_2}{T_1} \]
Where:
- \( V_1 = 1 \, L \) (initial volume)
- \( V_2 \) is the final volume we need to find.

### Step 4: Substitute the known values into the equation
Now, substituting the values we have:
\[ \frac{V_2}{1 \, L} = \frac{570 \, K}{300 \, K} \]

### Step 5: Solve for the final volume \( V_2 \)
Now, we can solve for \( V_2 \):
\[ V_2 = 1 \, L \times \frac{570}{300} \]
\[ V_2 = \frac{570}{300} \, L \]
\[ V_2 = 1.9 \, L \]

### Conclusion
The final volume of the gas after heating is approximately \( 1.9 \, L \).