Chapter 4.8, Problem 19P

(A)

Interpretation Introduction

Interpretation:

Determine the final temperature of the block when system reaches equilibrium.

Concept Introduction:

Write the steady state energy balance equation for copper block.

$\frac{d}{dt}\left\{M\left(\widehat{U}+\frac{V^2}{2}+gh\right)\right\}=\left[\begin{array}{l}{m}_{in}\left({\widehat{H}}_{in}+\frac{V_{in}^2}{2}+g{h}_{in}\right)-m_{out}\left({\widehat{H}}_{out}+\frac{V_{out}^2}{2}+g{h}_{out}\right)\\ +W_{\text{S}}+W_{\text{EC}}+Q\end{array}\right]$

Here, time is $t$, total mass is $M$, specific internal energy is $\widehat{U}$, velocity is $V$, acceleration due to gravity is $g$, height is $h$, initial mass flow is $m_{in}$, initial specific enthalpy is ${\widehat{H}}_{in}$, heat is added or removed from the system is $Q$, initial velocity is $V_{in}$, initial height of the gas is $h_{in}$, final mass flow is $m_{out}$, final height of the gas is $h_{out}$, shaft work is added to the system is $W_{\text{S}}$, and work is added to the system through expansion or contraction of the system is $W_{\text{EC}}$.

(B)

Interpretation Introduction

Interpretation:

Determine the change in entropy of the universe.

Concept Introduction:

Write the formula to calculate the change in entropy $\left(d{S}_{copper}\right)$ in copper.

$\begin{array}{c}d{S}_{copper}=\frac{d{Q}_{rev}}{T}\\ =\frac{M_{copper}{C}_{V,copper}dT}{T}\end{array}$

Here, constant volume heat capacity in copper is $C_{V,copper}$, change in the reversible heat is $Q_{rev}$, and temperature is $T$.