A cylinder fitted with a frictionless movable piston contains 2 moles of an ideal gas at 27°C and a volume of 10 L. The gas is heated to 127°C while maintaining constant pressure. What will be the final volume of the gas?
13.3 L
To determine the final volume of the gas when heated from 27°C to 127°C at constant pressure, we can use Charles's Law. Charles's Law states that the volume of an ideal gas is directly proportional to its temperature at constant pressure. This can be expressed with the formula:
V_1/T_1 = V_2/T_2
where:
- V_1 is the initial volume of the gas.
- T_1 is the initial temperature in Kelvin.
- V_2 is the final volume of the gas.
- T_2 is the final temperature in Kelvin.
Step 1: Convert temperatures from Celsius to Kelvin.
T_1 = 27 + 273 = 300 \, \text{K}
T_2 = 127 + 273 = 400 \, \text{K}
Step 2: Use Charles's Law to find the final volume.
Given:
- V_1 = 10 \, \text{L}
Using the relation:
\frac{V_1}{T_1} = \frac{V_2}{T_2}
Plug in the values:
\frac{10}{300} = \frac{V_2}{400}
Solve for V_2:
V_2 = \frac{10 \times 400}{300}
V_2 = \frac{4000}{300} = 13.33 \, \text{L}
Therefore, the final volume of the gas when heated to 127°C at constant pressure is 13.3 L.
This matches the correct option.
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