To what temperature must a gas be raised from \(313 \mathrm{~K}\) so as to double both its volume and pressure?
A. \(1252 \mathrm{~K}\)
B. \(313 \mathrm{~K}\)
C. \(626 \mathrm{~K}\)
D. \(1252^{\circ} \mathrm{C}\)
Correct Answer: A
Explanation
\begin{array}{l}
T_1=313 \mathrm{~K}, P_1=P, V_1=V, T_2=?, P_2=2 P \\
V_2=2 \mathrm{~V}
\end{array}
Using the general gas equation,
\(\frac{P_1 V_1}{T_1}=\frac{P_2 V_2}{T_2}\)
\(\frac{P \times V}{131}=\frac{2 P \times 2 V}{T_2}\)
\(T_2=\frac{313 \times 2 P \times 2 V}{P \times V}=(313 \times 2 \times 2) \mathrm{K}\)
\(=1252 \mathrm{~K}\)
