Chapter 11, Problem 11.1YT

Interpretation Introduction

Interpretation:

The volume of the crumpled can is to be calculated.

Concept Introduction:

According to the Boyle’s law the pressure and volume of a gas are inversely proportional.

According to Boyle’s law, for a constant temperature and quantity of gas, the relation between pressure and volume is as follows:

$P_1{V}_1=P_2{V}_2$.….. (1)

Here, $P_1$ is the initial pressure, $V_1$ is the initial volume, $P_2$ is the final pressure and $V_2$ is the final volume.

Answer to Problem 11.1YT

Solution: $0.5\text{ L}$

Explanation of Solution

Given information:

The initial volume of gasoline is $2.0\text{ L}$, the pressure at sea level is $1.0\text{ atm}$ and the pressure of water is $4.0\text{ atm}$.

Boyle’s law gives the relation between the volume and temperature of a gas as follows:

$P_1{V}_1=P_2{V}_2$

Rearrange the above expression for $V_2$ as follows:

$V_2=\frac{P_1{V}_1}{P_2}$

Substitute $1.0\text{ atm}$ for $P_1$, $2.0\text{ L}$ for $V_1$ and $4.0\text{ atm}$ for $P_2$ in the above expression:

$\begin{array}{c}{V}_2=\frac{\left(1.0\cancel{\text{atm }}\right)\left(2.0\text{L}\right)}{4.0\cancel{\text{atm}}}\\ =0.5\text{ L}\end{array}$

Conclusion

The volume of the crumpled can is $0.5\text{ L}$.