# 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?

Dec 5, 2015

50˚"C"

#### Explanation:

Use the formula: $\frac{{P}_{1} {V}_{1}}{{T}_{1}} = \frac{{P}_{2} {V}_{2}}{{T}_{2}}$

We know that we want ${P}_{1} = {P}_{2}$ so the pressure will remain constant, so we can say that: $\frac{\textcolor{b l u e}{{P}_{1}} {V}_{1}}{{T}_{1}} = \frac{\textcolor{b l u e}{{P}_{1}} {V}_{2}}{{T}_{2}}$

Plug in the values we know: $\frac{{P}_{1} \cdot 0.250 \text{L")/(283"K")=(P_1*0.285"L}}{{T}_{2}}$
(Remember that temperature must be done in Kelvin.)

Cross multiply: ${T}_{2} \cdot {P}_{1} \cdot 0.250 \text{L"=283"K"*P_1*0.285"L}$

Divide both sides by ${P}_{1}$.

${T}_{2} \cdot 0.250 \text{L"=283"K"*0.285"L}$

${T}_{2} = \left(283 \text{K"*0.285"L")/(0.250"L}\right)$

${T}_{2} = 323 \text{K}$

(This is also 50˚"C".)