Solved: An air pistol contains compressed air in a small

Chapter 3, Problem 283EUP

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QUESTION:

Problem 283EUP

An air pistol contains compressed air in a small cylinder, as shown in Fig. P3.164. Assume that the volume is 1 in.3, pressure is 10 atm, and the temperature is 80 F when armed. A bullet, m = 0.04 lbm, acts as a piston initially held by a pin (trigger); when released, the air expands in an isothermal process (T = constant). If the air pressure is 1 atm in the cylinder as the bullet leaves the gun, find

a. the final volume and the mass of air.

b. the work done by the air and work done on the atmosphere.

c. the work to the bullet and the bullet’s exit velocity.

FIGURE P3.164

Questions & Answers

QUESTION:

Problem 283EUP

An air pistol contains compressed air in a small cylinder, as shown in Fig. P3.164. Assume that the volume is 1 in.3, pressure is 10 atm, and the temperature is 80 F when armed. A bullet, m = 0.04 lbm, acts as a piston initially held by a pin (trigger); when released, the air expands in an isothermal process (T = constant). If the air pressure is 1 atm in the cylinder as the bullet leaves the gun, find

a. the final volume and the mass of air.

b. the work done by the air and work done on the atmosphere.

c. the work to the bullet and the bullet’s exit velocity.

FIGURE P3.164

ANSWER:

Solution 283 EUP:

Step 1 of 3:-

The volume of the small cylinder is,

.

The pressure inside is, .

The temperature is,

.

The mass of the bullet is,

.

The air expands by keeping the temperature constant.

When the bullet left the gun, the pressure became,

.

  1. Here we have to find the final volume and mass of the air.

By the ideal gas approximation,

     .

So, the mass of air inside is 0.038 lbm.

For the volume, again we can apply the same law at constant temperature.

So, the final volume will be .

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