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

A. 0.0228938 m3

B. 0.0457875 m3

C. 0.5228938 m3

D. 0.5457875 m3

To solve this we assume that the gas inside the balloon is an ideal gas. Then, we can use the ideal gas equation which is expressed as PV = nRT. At a constant pressure and number of moles of the gas the ratio T/V is equal to some constant. At another set of condition of temperature, the constant is still the same. Calculations are as follows:

T1 / V1 = T2 / V2

V2 = T2 x V1 / T1

V2 = 318.15 x 0.5 / 293.15

V2 = 0.5457875 m³