# How hot would a 2.3 L balloon have to get to expand to a volume of 3.0 L, assuming the initial temperature of the balloon is 24°C, and that the pressure inside the balloon remains constant?

Jan 31, 2016

The temperature needs to be 390 K.

#### Explanation:

This is an example of Charles' law, which states that the volume of a gas held at constant pressure varies directly with the Kelvin temperature. The equation for this law is:

${V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}$

Given/Known
${V}_{1} = \text{2.3 L}$
${T}_{1} = {24}^{\circ} \text{C"+273.15="297 K}$
${V}_{2} = \text{3.0 L}$

Unknown
${T}_{2}$

Solution
Rearrange the equation to isolate ${T}_{2}$, substitute the values into the equation and solve.

${V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}$

${T}_{2} = \frac{{T}_{1} {V}_{2}}{{V}_{1}}$

T_2=((297"K")xx(3.0"L"))/(2.3"L")

${T}_{2} = \text{390 K}$ rounded to two significant figures.