Determine the constant of variation for the stated condition.
-The volume $\mathrm { V }$ of a given mass of gas varies directly as the temperature $\mathrm { T }$ and inversely as the pressure $\mathrm { P }$. A measuring device is calibrated to give $\mathrm { V } = 216 \mathrm { in } ^ { 3 }$ when $\mathrm { T } = 450 ^ { \circ }$ and $\mathrm { P } = 25 \mathrm { lb } / \mathrm { in } ^ { 2 }$. What is the volume on this device when the temperature is $500 ^ { \circ }$ and the pressure is $20 \mathrm { lb } / \mathrm { in } ^ { 2 } ?$
A) $V = 300$ in $^ { 3 }$
B) $\mathrm { V } = 25 \mathrm { in } ^ { 3 }$
C) $V = 320$ in $^ { 3 }$
D) $V = 280$ in $^ { 3 }$

Question

Quizplus · Accepted Answer

The volume $V$ varies directly as the temperature $T$ and inversely as the pressure $P$, so $V = k \frac{T}{P}$ for some constant $k$. Using the given calibration, $216 = k \frac{450}{25}$. Solving for $k$ gives $k = 12$. For $T = 500^\circ$ and $P = 20 \, \text{lb/in}^2$, $V = 12 \frac{500}{20} = 300 \, \text{in}^3$.

Determine the Constant of Variation for the Stated Condition V\mathrm { V }V

Determine the Constant of Variation for the Stated Condition $\mathrm { V }$