Question

A balloon is inflated in a warm living room (24oC) to a volume of 2.5L. It was taken
out on a very cold winter day (-30oC). Assuming that mass of air and pressure inside
the balloon are constant, find out the volume of the balloon.

Answer 1

Answer:-

Given:

Initial Volume $\sf({V_1})$ = 2.5 L

Initial Temperature $\sf({T_1})$ = 24° C + 273.15 = 297.15 ° K.

Final Temperature $\sf{(T_2)}$ = - 30° C + 273.15 = 243.15 ° K.

We know that,

Charley's law of gases states that at constant pressure the temperature of the gas is directly proportional to its Volume.

→ V = kT (k is constant)

→ VT = k

$→\sf{ \frac{ V_{1} }{T _{1} } = \frac{V _{2} }{T_{2} } } \\ \\ →\sf{ \frac{2.5}{297.15} = \frac{ V_{2} }{243.15} } \\ \\ →\sf{V_{2} = \frac{243.15 \times 2.5}{297.15} } \\ \\→ \sf\large{ V_{2} = 2 \: L}$

Hence, the Volume of the balloon will be 2 L.