At 10°C, the gas in a cylinder has a volume of 0.250 L. The gas is allowed to expand to 0.285 L. What must the final temperature be for the pressure to remain constant?

1 Answer
Dec 5, 2015

#50˚"C"#

Explanation:

Use the formula: #(P_1V_1)/(T_1)=(P_2V_2)/(T_2)#

We know that we want #P_1=P_2# so the pressure will remain constant, so we can say that: #(color(blue)(P_1)V_1)/(T_1)=(color(blue)(P_1)V_2)/(T_2)#

Plug in the values we know: #(P_1*0.250"L")/(283"K")=(P_1*0.285"L")/(T_2)#
(Remember that temperature must be done in Kelvin.)

Cross multiply: #T_2*P_1*0.250"L"=283"K"*P_1*0.285"L"#

Divide both sides by #P_1#.

#T_2*0.250"L"=283"K"*0.285"L"#

#T_2=(283"K"*0.285"L")/(0.250"L")#

#T_2=323"K"#

(This is also #50˚"C"#.)