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?

1 Answer
Mar 11, 2016

Answer:

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"#