Chapter 19, Problem 1DQ

(a)

To determine

Whether the work done by the system on the environment is positive or negative for the expansion of the burned gasoline-air mixture in the cylinder of an automobile engine.

Explanation of Solution

Work done by the system on the environment for the expansion of the burned gasoline-air mixture in the cylinder of an automobile engine is positive.

Formula to calculate the Work done by the system,

$W=p\left(V_2-V_1\right)$

• $W$ is the work done by the system
• $p$ is the pressure of the system
• $V_2$ is the final volume of the system
• $V_1$ is the initial volume of the system

The final volume of the gasoline-air mixture in the cylinder increases. Therefore change in the volume of the cylinder has a positive value.

$\left(V_2-V_1\right)=+\text{ve}$

Therefore the work done by the burned gasoline-air mixture on the environment is positive.

Conclusion:

Work done by the system on the environment for the expansion of the burned gasoline-air mixture in the cylinder of an automobile engine is positive.

(b)

To determine

Whether the work done by the system on the environment on the environment positive or negative for the opening a bottle of champagne.

Explanation of Solution

The work done by the system on the environment is positive for opening a bottle of champagne.

Formula to calculate the Work done by the system,

$W=p\left(V_2-V_1\right)$

• $W$ is the work done by the system
• $p$ is the pressure of the system
• $V_2$ is the final volume of the system
• $V_1$ is the initial volume of the system

The final volume of the champagne increases as the bottle of champagne is opened. Therefore the change in volume for the champagne has a positive value.

$\left(V_2-V_1\right)=+\text{ve}$

Consequently, work done by the champagne bottle on the environment is positive.

Conclusion:

Therefore, the work done by the system on the environment is positive for opening a bottle of champagne.

(c)

To determine

Whether the work done by the system on the environment on the environment positive or negative for filling a scuba tank with compressed air.

Explanation of Solution

The work done by the system on the environment on the environment is negative for filling a scuba tank with compressed air.

Formula to calculate the Work done by the system,

$W=p\left(V_2-V_1\right)$

• $W$ is the work done by the system
• $p$ is the pressure of the system
• $V_2$ is the final volume of the system
• $V_1$ is the initial volume of the system

The final volume of the scuba tank decreases while filling it with a compressed air. Therefore change in volume of the tank has a negative value.

$\left(V_2-V_1\right)=-\text{ve}$

Consequently, the work done by the scuba tank on the environment is negative.

Conclusion:

Therefore, the work done by the scuba tank on the environment is negative as final volume of the tank decreases.

(d)

To determine

Whether the work done by the system on the environment on the environment positive or negative for partial crumpling of a sealed, empty water bottle as you drive from the mountains down to sea level.

Explanation of Solution

The work done by the system on the environment on the environment negative for partial crumpling of a sealedas you drive from the mountains down to sea level.

Formula to calculate the Work done by the system,

$W=p\left(V_2-V_1\right)$

• $W$ is the work done by the system
• $p$ is the pressure of the system
• $V_2$ is the final volume of the system
• $V_1$ is the initial volume of the system

The final volume of the gas in the empty bottle decreases due to the increase in the pressure while driving from the mountains to sea level. Therefore change in volume of the gas in the empty bottle has a negative value.

$\left(V_2-V_1\right)=-\text{ve}$

Consequently, the work done by the gas in the empty bottle on the environment is negative.

Conclusion:

Therefore, the work done by the gas in the empty bottle on the environment is negative as final volume of the tank decreases.