# A balloon has a volume of 0.5 L at 20°C. What will the volume be if the balloon is heated to 150°C?

## Assume constant pressure and mass.

Dec 26, 2016

Assuming pressure is constant:

#### Explanation:

${V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}$ ($T$ in Kelvin)

${20}^{o} C = 20 + 273 = 293 K$
${150}^{o} C = 150 + 273 = 423 K$

$\frac{0.5}{293} = {V}_{2} / 423 \to {V}_{2} = \frac{0.5 \times 423}{293} = 0.72 L$

Dec 26, 2016

The new volume will be $\text{0.7 L}$.

#### Explanation:

This is an example of Charles' law, sometimes called the temperature-volume law. It states that the volume of a gas is directly proportional to the Kelvin temperature, while pressure and amount are held constant.

The equation is ${V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}$, where $V$ is volume and $T$ is temperature in Kelvins.

Known
${V}_{1} = \text{0.5 L}$
${T}_{1} = \text{20"^@"C"+273.15="293 K}$
${T}_{2} = \text{150"^@"C"+273.15="423 K}$

Unknown
${V}_{2}$

Solution
Rearrange the equation to isolate ${V}_{2}$. Substitute the known values into the equation and solve.

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

V_2=((0.5"L"xx423"K"))/(293"K")="0.7 L" rounded to one significant figure