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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??

Sagot :

Step 1; Identify the quantites

volume = V

Temperature = T

Pressure = P

[tex]\begin{gathered} V\text{ }\infty\frac{T}{P} \\ V\text{ = K }\frac{T}{P} \\ \text{Where K = constant of variation} \end{gathered}[/tex]

V = 645, T = 430°, P = 10

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

[tex]\begin{gathered} 645\text{ = k (}\frac{430}{10}) \\ 645\text{ = K (43)} \\ K\text{ = }\frac{645}{43} \\ K\text{ = 15} \end{gathered}[/tex]

The relationship between the variables is given as

[tex]V\text{ = 15}\frac{T}{P}[/tex]

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

Then substitute the values into the relationship to find V

[tex]\begin{gathered} V\text{ = 15(}\frac{100}{20}) \\ V\text{ = }\frac{1500}{20} \\ V=\text{7}5 \end{gathered}[/tex]

Therefore , volume V is 75

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