Chapter 2.6, Problem 18P

(A)

Interpretation Introduction

Interpretation:

The final pressure of the gas.

Concept Introduction:

The expression to obtain the pressure acting on the piston $\left(P_W\right)$.

$\begin{array}{c}{P}_W=\frac{F}{A}\\ =\frac{ma}{\frac{\pi }{4}{D}^2}\end{array}$

Here, additional weight on the piston-cylinder is m, acceleration due to gravity is a, and diameter of piston-cylinder device is D.

Write the expression to obtain the final pressure of gas $\left(P\right)$.

$P=P_W+P_{atm}$

Here, atmospheric pressure is $P_{\text{atm}}$ and weight pressure is $P_W$.

(B)

Interpretation Introduction

Interpretation:

The final volume of the gas.

Concept Introduction:

The expression of ideal gas law.

$PV=NRT$

Here, number of moles of gas is N, gas constant is R, temperature is T, and pressure is P.

(C)

Interpretation Introduction

Interpretation:

The work done on the gas during the process.

Concept Introduction:

The expression of pressure in terms of volume using ideal gas law.

$P_1=\frac{NRT}{V_1}$

$V_1=\frac{NRT}{P_1}$

Here, initial pressure is $P_1$.

The expression of work of expansion and contraction.

$W_{EC}=-{\displaystyle \int PdV}$