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

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

Explanation

Step 1

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

$\begin{gathered} V=\alpha\frac{T}{P} \\ \text{where}\alpha\text{ is a constant} \end{gathered}$

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

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

no, rewrite the equation

$\begin{gathered} V=\alpha\frac{T}{P} \\ V=12\frac{T}{P} \end{gathered}$

Step 2

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

replace

$\begin{gathered} V=12\frac{T}{P} \\ V=12\frac{320}{20\frac{lb}{In^2}} \\ V=192\text{ cubic inches} \end{gathered}$

I hope this helps you