Question

If I want a 7.63 L balloon at an initial temperature of 27.00 C to expand to a volume of 40.0L,

what would the temperature have to be?

Answer 1

PV=nRT - the formula of Mendeleev-Clapeyron. (Important T=t+273 is the absolute temperature, where t is the temperature in Celsius units.)

For simplicity, we assume that the pressure does not change in the atmosphere outside the ball, and as the volume of the ball increases, the tension of its walls changes slightly. Then, in the first approximation, the pressure inside the ball remains constant.

P=const

So, V₁/T₁=V₂/T₂ , or T₂/T₁=V₂/V₁

T₂=T₁V₂/V₁=(27+273)K*40L/7.63L=1573K or 1300^oC

Answer: 1300^oC