Question

Triple expansion steam engines were used extensively to power ocean liners like the Titanic. They worked via high steam pressure that was gradually decreased as it travelled from one cylinder to another due to the principles of Charles’ law. The first cylinder was the smallest and the last had the largest volume. If it enters the first cylinder (100 Liters) at 18.9 atm and exits the last at 1.7 atm, what is its final Volume?

Answer 1

Given

$\begin{gathered} P_1=18.9\text{ atm} \\ V_1=100\text{ L} \\ P_2=1.7\text{ atm} \end{gathered}$

The ideal gas equation is given as,

$PV=nRT$

Here, n is the number of moles, R is the universal gas constant and T is the temperature (constant).

Therefore,

$PV=\text{const}$

Hence,

$P_1V_1=P_2V_2$

Therefore, the final volume V_2 is given as,

$V_2=\frac{P_1V_1}{P_2}$

Substituting all known values,

$\begin{gathered} V_2=\frac{18.9\text{ atm}\times100\text{ L}}{1.7\text{ atm}} \\ =1111.76\text{ L} \end{gathered}$

Therefore, the final volume is 1111.76 L.