# A balloon has a volume of 253.2 mL at 356 K. The volume of the balloon is decreased to 165.4 mL. What is the new temperature?

Nov 19, 2015

The new temperature is $\text{233 K}$.

#### Explanation:

Charles' law states that when pressure is held constant, temperature and volume are directly proportional. The equation to use is ${V}_{1} / {T}_{1} {V}_{2} / {T}_{2}$.

Given
${V}_{1} = 252.3 \cancel{\text{mL"xx(1"L")/(1000cancel"mL")="0.2523 L}}$
${T}_{1} = \text{356 K}$
${V}_{2} = 165.4 \cancel{\text{mL"xx(1"L")/(1000cancel"mL")="0.1654 L}}$

Unknown
${T}_{2}$

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

Solution
Rearrange the equation to isolate ${T}_{2}$.
${T}_{2} = \frac{{T}_{1} {V}_{2}}{V} _ 1$

T_2=((356"K")xx(0.1654cancel"L"))/(0.2523cancel"L")="233 K"