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A mass of gas under constant pressure occupies a volume of 0.5 m3 at a temperature of 20 degree Celsius. Using the formula for cubic expansion, what will be the volume at a temperature of 45 degree Celsius without a change in pressure?

A0.5228938 m3
B0.0228938 m3
C0.5457875 m3
D0.0457875 m3

Verified Answer :

the answer is C 0.5457875

Answer: C) 0.5457875 \(m^3\)

Explanation: Charles' Law: This law states that volume is directly proportional to the temperature of the gas at constant pressure and number of moles.

\(V\propto T\)    (At constant pressure and number of moles)

\(\frac{V_1}{T_1}=\frac{V_2}{T_2}\)

where,

\(V_1\) = initial volume of gas = \(0.5m^3\)

\(T_1\) = initial temperature of gas =\(20^oC=273.15+20=293.15K\)

\(V_2\) = final volume of gas = 0?

\(T_2\) = final temperature of gas = \(45^oC=273.15+45=318.15K\)

\(\frac{0.5}{293.15}=\frac{V_2}{318.15}\)

\(V_2=0.5457875m^3\)

Thus the final volume is \(0.5457875m^3\)

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