Answer:
B. [tex]V_{f}= 10\,cubic\,inches [/tex]
Explanation:
Assuming we are dealing with a perfect gas, we should use the perfect gas equation:
[tex]PV=nRT [/tex]
With T the temperature, V the volume, P the pressure, R the perfect gas constant and n the number of mol, we are going to use the subscripts i for the initial state when the gas has 20 cubic inches of volume and absolute pressure of 5 psi, and final state when the gas reaches 10 psi, so we have two equations:
[tex]P_{i}V_{i}=n_{i}RT_{i} [/tex] (1)
[tex] P_{f}V_{f}=n_{f}RT_{f}[/tex] (2)
Assuming the temperature and the number of moles remain constant (number of moles remain constant if we don't have a leak of gas) we should equate equations (1) and (2) because [tex] T_{i}=T_{f}[/tex], [tex]n_{i}=n_{f} [/tex] and R is an universal constant:
[tex]P_{i}V_{i}= P_{f}V_{f} [/tex], solving for [tex]V_{f} [/tex]
[tex]V_{f} =\frac{P_{i}V_{i}}{P_{f}} =\frac{(5)(20)}{10} [/tex]
[tex]V_{f}= 10 cubic\,inches [/tex]
