Question

20 cubic inches of a gas with an absolute pressure of 5 psi is compressed until its pressure reaches 10 psi. What's the new volume of the gas? (Assume that there's no change in temperature.)A. 100 cubic inchesB. 10 cubic inchesC. 40 cubic inchesD. 5 cubic inches

Answer 1

B.
`V_(f)= 10\,cubic\,inches`

Step-by-step explanation:

Assuming we are dealing with a perfect gas, we should use the perfect gas equation:

`PV=nRT`

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:

`P_(i)V_(i)=n_(i)RT_(i)` (1)

`P_(f)V_(f)=n_(f)RT_(f)` (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
`T_(i)=T_(f)`,
`n_(i)=n_(f)` and R is an universal constant:

`P_(i)V_(i)= P_(f)V_(f)`, solving for
`V_(f)`

`V_(f) =(P_(i)V_(i))/(P_(f)) =((5)(20))/(10)`

`V_(f)= 10 cubic\,inches`