Question

) The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P. A measuring device is calibrated to give V = 124.8 in3 when T = 260° and P = 25 lb/in2 What is the volume on this device when the temperature is 320° and the pressure is 20 lb/in27 A) V = 16 in3 B) V = 162 in 3 C) V = 192 in 3 D) V = 222 in 3

Answer 1

`\begin{gathered} C)V=192\text{ cubic inches} \\ \end{gathered}`

Step-by-step explanation

Step 1

The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P

`\begin{gathered} V=\alpha(T)/(P) \\ \text{where}\alpha\text{ is a constant} \end{gathered}`

A measuring device is calibrated to give V = 124.8 in3 when T = 260° and P = 25 lb/in2 ,we can use this info to get the constant

`\begin{gathered} V=\alpha(T)/(P) \\ 124.8in^3=\alpha(260)/(25(lb)/(In^2)) \\ 124.8=(\alpha260)/(25) \\ (124.8\cdot25)/(260)=\alpha \\ so,\text{ } \\ \alpha=12 \end{gathered}`

no, rewrite the equation

`\begin{gathered} V=\alpha(T)/(P) \\ V=12(T)/(P) \end{gathered}`

Step 2

What is the volume on this device when the temperature is 320° and the pressure is 20 lb/in2

replace

`\begin{gathered} V=12(T)/(P) \\ V=12(320)/(20(lb)/(In^2)) \\ V=192\text{ cubic inches} \end{gathered}`

I hope this helps you