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?

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Answer 1 · 2015-12-05T16:34:11

$50˚"C"$

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 $50˚"C"$ .)