Question

The pressure of 250 kPa acting on 15 cubic meters of gas at a temperature of 100 K is increased to 500 kPa and the volume is increased to 30 cubic meters. What is the temperature of the gas at this new pressure and volume?

Answer 1

The final temperature will be 400 K.

Explanation:

This is an example of the combined gas law. The equation to use is `(P_1V_1)/(T_1)=(P_2V_2)/(T_2)`.

Given
Initial pressure, `P_1="250 kPa"`
Initial volume, `V_1="15 m"^3"`
Initial temperature, `T_1="100 K"`
Final pressure, `P_2="500 kPa"`
Final volume, `V_2="30 m"^3"`

Unknown
Final temperature, `T_2`

Solution
Rearrange the equation to isolate `T_2`. Substitute the given values into the equation and solve.

`(P_1V_1)/(T_1)=(P_2V_2)/(T_2)`

`T_2=(T_1P_2V_2)/(P_1V_1)`

`T_2=(100"K"·500cancel"kPa"·30cancel"m"^3)/(250cancel"kPa"·15cancel"m"^3)="400K"`