# The gas inside of a container exerts 18 Pa of pressure and is at a temperature of 360 ^o K. If the pressure in the container changes to 24 Pa with no change in the container's volume, what is the new temperature of the gas?

Oct 6, 2017

 T_2 = 480’K

#### Explanation:

Start with the Ideal Gas Law: $P \cdot V = \left(n \cdot R \cdot T\right)$
The only parameter that needs a specific unit for correct calculations is the Temperature, in ‘K. The other parameters are ratios. We already have the data in the proper temperature units, so we can use the Gas Law to calculate the change in the temperature from the change in the pressure ratio.

The volume is constant in this case, and the gas constant is constant, so we only need the equation that shows the change in pressure with respect to temperature (T) for a calculation of the ratio change.
${P}_{2} / {P}_{1} = \left({T}_{2} / {T}_{1}\right)$ ; ${T}_{2} = \left({P}_{2} / {P}_{1}\right) \times {T}_{1}$; ${T}_{2} = 360 \times \left(\frac{24}{18}\right)$

 T_2 = 480’K