At -40°C, a sample of gas has a volume of 233 mL. On heating, the volume expands to 313 mL. Assuming constant pressure, what is the new Celsius temperature?

Md Ariful Islam

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This isthe an example of which states the volume of a gas that is held at a constant pressure varies directly with the Kelvin temperature. The formula used to solve this problem is $V_1/T_1=V_2/T_2$.

Given/Known
$V_1="233 mL"$
$T_1=-40^"o""C"+273.15="233 K"$
$V_2="313 mL"$

Unknown
$T_2$ in degrees C

Solution
Rearrange the equation to isolate $T_2$ and solve.

$V_1/T_1=V_2/T_2$

$T_2=(V_2T_1)/V_1$

$T_2=(313cancel"mL"xx233"K")/(233cancel"mL")="313 K"$

Convert temperature in Kelvins to degrees Celsius.

$""^"o""C"="K-273.15"$

$""^"o""C"=313 "K"-273.15=40""^"o""C"$ (rounded to a whole number)

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