The volume $\mathrm { V }$ of a given mass of gas varies directly as the temperature $\mathrm { T }$ and inversely as the pressure $\mathrm { P }$. If $\mathrm { V } = 121.0$ in. ${ } ^ { 3 }$ when $\mathrm { T } = 110 ^ { \circ }$ and $\mathrm { P } = 10 \mathrm { lb } /$ in. 2 , what is the volume when $\mathrm { T } = 380 ^ { \circ }$ and $P = 15 \mathrm { lb } /$ in. $^ { 2 }$ ? (Round to the nearest tenth.)
A) $278.7 \mathrm { in. } ^ { 3 }$
B) $258.7 \mathrm { in. } ^ { 3 }$
C) $318.7$ in. 3
D) $238.7 \mathrm { in. } ^ { 3 }$

Question

Quizplus · Accepted Answer

The volume of a gas is given by $V = k \frac{T}{P}$, where $k$ is a constant. Using the initial conditions, we can find $k$ and then calculate the new volume with the given $T$ and $P$. The correct calculation leads to a volume of approximately $278.7 \, \text{in}^3$.

The Volume V\mathrm { V }V Of a Given Mass of Gas Varies Directly as the of Gas

The Volume $\mathrm { V }$ Of a Given Mass of Gas Varies Directly as the of Gas