How hot must the air become in order to increase the volume to 4.5 x 10^2 liters?

Question

The hot air balloon is filled with 1.89 x 10^2 liters of air at 21 degrees C. The atmospheric pressure is consistent for this problem.

Answer 1

V is proportional to T. T in kelvins, = 273.2 + T in deg Celsius.

So the original T is 294.2. Solve for new T like this from proportions:

(T/294.2) = 4.5/1.89 Note, the 10²s in numerator and denominator cancel each other.

T = 700.476 kelvins

= 427.3 deg Celsius

Technically, you'd round off to 2 sig figs because of 4.5.