Question

A cylinder of gas is compressed by a piston from an initial volume of 125 liters to a final volume of 90 liters. The compression occurs at constant pressure, and the work done on the gas by the piston is 104 joules. What is the gas pressure during the compression? (1 liter = 10-3 meters3)
A.
4 × 102 pascals
B.
3 × 105 pascals
C.
1 × 105 pascals
D.
3 × 104 pascals
E.
3 × 10-1 pascals

Answer 1

A pascal is a unit of pressure, and we know that pressure is Force ÷ Area.  Now let us derive an equation that has Energy and Volume:

$P=\frac{Force}{Area}=\frac{Force \times Distance}{Area \times Distance}=\frac{Work}{Volume}$

Now we want to calculate the difference in volume and so:

$V_{initial}-V_{final}=125l-90l=35l$

Now since $1l=1x10^{-3}m$ we have:

$35l \times \frac{1}{10\timesm^3}= 0.035m^{-3}$

Therefore we can now calculate the pressure:

$P=\frac{Work}{Volume}=\frac{104J}{0.035m^3}=2971.43 pa \approx 3 \times 10^{3}pa$