Chapter 1.7, Problem 29P

A)

Interpretation Introduction

Interpretation:

The work done by the balloon on the surrounding if the pressure $\left(P\right)$ of $\text{1}\text{bar}$ opposing the expansion has to be determined.

Concept introduction:

The integral form of expansion of work $\left(W_{EC}\right)$.

$\begin{array}{c}{W}_{EC}=-{\displaystyle \underset{V_{\text{initial}}}{\overset{V_{\text{final}}}{\int }}PdV}\\ =-P\left(V_{\text{final}}-V_{\text{initial}}\right)\end{array}$

Here, constant pressure is P, initial and final volume is $V_{\text{initial}}\text{and}{V}_{\text{final}}$ respectively.

Since initial volume is negligible, substitute $0$ for $V_{\text{initial}}$ in Equation (1).

$\begin{array}{c}{W}_{EC}=-P\left(V_{\text{final}}-0\right)\\ W_{EC}=-P{V}_{\text{final}}\end{array}$

B)

Interpretation Introduction

Interpretation:

The work done by the balloon on the surrounding if the pressure $\left(P\right)$ of $\text{0}\text{.5}\text{bar}$ opposing the expansion has to be determined

Concept introduction:

The integral form of expansion of work $\left(W_{EC}\right)$.

$\begin{array}{c}{W}_{EC}=-{\displaystyle \underset{V_{\text{initial}}}{\overset{V_{\text{final}}}{\int }}PdV}\\ =-P\left(V_{\text{final}}-V_{\text{initial}}\right)\end{array}$

Here, constant pressure is P, initial and final volume is $V_{\text{initial}}\text{and}{V}_{\text{final}}$ respectively.

Since initial volume is negligible, substitute $0$ for $V_{\text{initial}}$ in Equation (1).

$\begin{array}{c}{W}_{EC}=-P\left(V_{\text{final}}-0\right)\\ W_{EC}=-P{V}_{\text{final}}\end{array}$

C)

Interpretation Introduction

Interpretation:

The work done by the balloon on the surrounding if the pressure $\left(P\right)$ of $\text{0}\text{bar}$ opposing the expansion has to be determined

Concept introduction:

The integral form of expansion of work $\left(W_{EC}\right)$.

$\begin{array}{c}{W}_{EC}=-{\displaystyle \underset{V_{\text{initial}}}{\overset{V_{\text{final}}}{\int }}PdV}\\ =-P\left(V_{\text{final}}-V_{\text{initial}}\right)\end{array}$

Here, constant pressure is P, initial and final volume is $V_{\text{initial}}\text{and}{V}_{\text{final}}$ respectively.

Since initial volume is negligible, substitute $0$ for $V_{\text{initial}}$ in Equation (1).

$\begin{array}{c}{W}_{EC}=-P\left(V_{\text{final}}-0\right)\\ W_{EC}=-P{V}_{\text{final}}\end{array}$

D)

Interpretation Introduction

Interpretation:

The work done by the balloon on the surrounding if the pressure $\left(P\right)$ of $\text{3}\text{bar}$ opposing the expansion has to be determined

Concept introduction:

The integral form of expansion of work $\left(W_{EC}\right)$.

$\begin{array}{c}{W}_{EC}=-{\displaystyle \underset{V_{\text{initial}}}{\overset{V_{\text{final}}}{\int }}PdV}\\ =-P\left(V_{\text{final}}-V_{\text{initial}}\right)\end{array}$

Here, constant pressure is P, initial and final volume is $V_{\text{initial}}\text{and}{V}_{\text{final}}$ respectively.

Since initial volume is negligible, substitute $0$ for $V_{\text{initial}}$ in Equation (1).

$\begin{array}{c}{W}_{EC}=-P\left(V_{\text{final}}-0\right)\\ W_{EC}=-P{V}_{\text{final}}\end{array}$

E)

Interpretation Introduction

Interpretation:

Find out the realistic situation for the surrounding pressure given in Part A to D.