# A container with a volume of 7 L contains a gas with a temperature of 420^o K. If the temperature of the gas changes to 360 ^o K without any change in pressure, what must the container's new volume be?

May 20, 2018

$6 L$

#### Explanation:

Given: constant pressure, volume of a gas = 7 L; " "T = 420 K. Temperature changes to $360 K$, what is the new volume?

The general gas law: $\frac{{P}_{1} {V}_{1}}{T} _ 1 = \frac{{P}_{2} {V}_{2}}{T} _ 2$ where Temperature is required to be in the units of Kelvin.

When the pressure is constant, we can use Charles' Law:

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

Solve for $\text{ "V_2: " } \frac{7}{420} = {V}_{2} / 360$

Use the cross-product to solve a/b = c/d; " "a*d = b*c

$420 {V}_{2} = 7 \cdot 360 = 2520$

$\frac{420 {V}_{2}}{420} = \frac{2520}{420} = 6$

${V}_{2} = 6 L$