Question

A quantity of gas has a volume of 0.20 cubic meter and an absolute temperature of 333 degrees kelvin. When the temperature of the gas is raised to 533 degrees kelvin, what is the new volume of the gas? (Assume that there's no change in pressure.)
A. 0.3198 m3
B. 0.0006 m3
C. 0.2333 m3
D. 0.2146 m3

Answer 1

   
$\displaystyle \\ \texttt{Notations: } \\ P = \texttt{pressure} \\ V = \texttt{volume} \\ T = \texttt{absolute temperature} \\ \\ \texttt{We use the formula: }~ \frac{P \times V}{T} = \texttt{constant} \\ \\ \frac{P_1 \times V_1}{T_1} = \frac{P_2 \times V_2}{T_2} \\ \\ P_1 = P_2 \\ \\ \Longrightarrow~~\frac{V_1}{T_1} = \frac{V_2}{T_2}\\\\ \Longrightarrow~V_2 =\frac{V_1 \times T_2}{T_1}= \frac{0.2~m^3 \times 533^oK}{333^oK}=\frac{106.6}{333}= 0.3(201)\approx \boxed{0,32~m^3}$