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

question 112

Multiple Choice

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 \(^ { 3 }\)