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 inches
B. 10 cubic inches
C. 40 cubic inches
D. 5 cubic inches

The correct answer is B) 10 cubic inches

Answer 1

PoVo = PfVf    Vf=PoVo/Pf  = 5*20/10 = 100/10 = 10 cubic inches

Answer 2

It is given that that initial volume of gas is 20 cubic inches.

The initial pressure is given as 5 psi.

The final pressure is given as 10 psi

We are asked to calculate the final volume.

Let initial and final volume of gas is denoted as $v_{1} \ and\ v_{2}$

Let the initial and final pressure of gas is denoted as $p_{1} \ and\ p_{2}$

As per the question the temperature of a gas is constant.

From Boyle's law we know that pressure of a given mass of a gas is inversely proportional to the applied volume at constant temperature.

Hence mathematically

                                $p\ \alpha\ \frac{1}{v}$

                                $pv=constant$

                                $p_{1} v_{1} =p_{2} v_{2}$

                                $v_{2} =\frac{p_{1}v_{1} }{p_{2} }$

Putting the values of these respective quantities as mentioned above we get-

                                  $v_{2} =\frac{5\ psi*20 cubic\ inches}{10\ psi}$

                                         $=10\ cubic\ inches$        [ans]