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=645 in3 when T = 430° and P=10 lb/in2. What is the volume on this device when the temperature is 100° and the pressure is 201b/in??

Answer 1

Step 1; Identify the quantites

volume = V

Temperature = T

Pressure = P

`\begin{gathered} V\text{ }\infty(T)/(P) \\ V\text{ = K }(T)/(P) \\ \text{Where K = constant of variation} \end{gathered}`

V = 645, T = 430°, P = 10

Step 2 : substitute the value above into the formula to find the value of K

`\begin{gathered} 645\text{ = k (}(430)/(10)) \\ 645\text{ = K (43)} \\ K\text{ = }(645)/(43) \\ K\text{ = 15} \end{gathered}`

The relationship between the variables is given as

`V\text{ = 15}(T)/(P)`

Step 3: Find the volume, when T = 100°, P = 20

Then substitute the values into the relationship to find V

`\begin{gathered} V\text{ = 15(}(100)/(20)) \\ V\text{ = }(1500)/(20) \\ V=\text{7}5 \end{gathered}`

Therefore , volume V is 75