A certain mass of a gas occupies a volume of 2 litres at STP.Keeping the pressure constant at what temperature would the gas occupy a volume of 4 litres-

Options

A. `546^(@)C`
B. `273^(@)C`
C. `100^(@)C`
D. `50^(@)C`

Answer

To solve the problem, we can use Charles's Law, which states that at constant pressure, the volume of a gas is directly proportional to its absolute temperature (in Kelvin). The formula 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 1: Identify the given values.**
- Initial volume \( V_1 = 2 \) liters
- Final volume \( V_2 = 4 \) liters
- Initial temperature \( T_1 = 273 \) K (which is the temperature at STP)

**Step 2: Rearrange the formula to find \( T_2 \).**
From Charles's Law, we can rearrange the equation to solve for \( T_2 \):

\[ T_2 = \frac{V_2 \cdot T_1}{V_1} \]

**Step 3: Substitute the known values into the equation.**
Now we can substitute the values we have into the rearranged equation:

\[ T_2 = \frac{4 \, \text{liters} \cdot 273 \, \text{K}}{2 \, \text{liters}} \]

**Step 4: Calculate \( T_2 \).**
Performing the calculation:

\[ T_2 = \frac{4 \cdot 273}{2} = \frac{1092}{2} = 546 \, \text{K} \]

**Step 5: Conclusion.**
The temperature at which the gas would occupy a volume of 4 liters at constant pressure is \( T_2 = 546 \, \text{K} \).

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