Chapter 1, Problem 1.18P

Interpretation Introduction

(a)

Interpretation:

The force in (lb_f) exerted on the gas through the atmosphere, the piston, and the weight should be calculated assuming there is no friction between cylinder and the piston.

Concept Introduction:

The area of cross-section of the cylinder can be calculated using the following formula:

  $\text{A = }\frac{\text{π}}{4}{\text{d}}^2$

Here, d is diameter of the cylinder.

The force exerted by atmosphere can be calculated as follows:

  ${\text{F}}_{\text{atmosphere}}{\text{= P}}_{\text{atm}}\text{×A}$

Here, ${\text{F}}_{\text{atmosphere}}$ is force exerted by atmosphere, ${\text{P}}_{\text{atm}}$is atmospheric pressure and A is area.

Also, force exerted by piston and weight can be calculated as follows:

${\text{F}}_{\text{piston and weight}}\text{= mg}$

Here, m is total mass of piston and weight and g is acceleration due to gravity.

Similarly, total force will be sum of atmospheric force and force exerted piston and weight.

Interpretation Introduction

(b)

Interpretation:

The pressure of the gas is psia should be determined.

Concept Introduction:

Pressure of gas can be calculated using the following formula:

  $P=\frac{F}{A}$

Here, F is total force and A is area.

Also, 1 psia= 1 lb_f/ft²

Interpretation Introduction

(c)

Interpretation:

The work done by the gas in ft/lb_f and the potential energy change of the piston and weight should be determined.

Concept Introduction:

The work done by the gas can be calculated using the following formula:

$\text{W = F}\times \Delta \text{l}$

Here, F is force and $\Delta \text{l}$ is distance moved by piston and weight.

Also, the change in potential energy of the piston and weight can be calculated as follows:

$\text{ΔP}\text{.E = mgΔl}$

Here, m is mass, g is acceleration due to gravity and $\Delta \text{l}$ is distance moved by piston and weight.