Chapter 2.6, Problem 20P

(A)

Interpretation Introduction

Interpretation:

The final pressure of the gas.

Concept Introduction:

Write the ideal gas law for states 1 and 2.

$\frac{P_1{V}_1}{P_2{V}_2}=\frac{N_{1}R{T}_1}{N_{2}R{T}_2}$

$\begin{array}{l}\frac{P_1}{P_2}=\frac{T_1}{T_2}\\ P_2=P_1\frac{T_2}{T_1}\end{array}$

Here, initial and final volume is $V_1\text{and}{V}_2$, initial and final temperature is $T_1\text{and}{T}_2$, number of moles in states 1 and 2 is $N_1$ and $N_2$, initial and final pressure is $P_1\text{and}{P}_2$ respectively.

(B)

Interpretation Introduction

Interpretation:

The final pressure of the gas.

Concept Introduction:

The van der Waals equation.

$P=\frac{RT}{\underset{\_}{V}-b}-\frac{a}{{\underset{\_}{V}}^2}$

Here, pressure is P, constants are a and b, molar volume is $\underset{\_}{V}$, gas constant is R, and temperature is T.

(C)

Interpretation Introduction

Interpretation:

For the cases in parts A and B, how much work is done by the gas on the surroundings?