A weather balloon is inflated to a volume of 25.4 L at a pressure of 743 mmHg and a temperature of 25.8 ∘C. The balloon rises in the atmosphere to an altitude where the pressure is 400. mmHg and the temperature is -13.0 ∘C. Assuming the balloon can freely expand, calculate the volume of the balloon at this altitude

41.45 l.

Explanation:

Using gas equation,

(P1V1)/T1 = (P2V2)/T2

P1 = initial pressure

= 743 mmhg

= 99.73 kPa

V1 = initial volume

= 25.4 l

T1 = initial absolute temperature

= 25.8 + 273.15

= 298.95 K

P2 = final pressure

= 400 mmhg

= 53.33 kPa

T2 = final absolute temperature

= 273.15 + (-13)

= 260.15 K

V2 = (99.73 * 25.5 * 260.15)/(298.95 * 53.33)

= 41.45 l.