Question

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?

Answer 1

`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"`.)