Homework set #$2$ due by Sep $7$

A gas is compressed from $V_1=0\mathrm{.}3m^3,p_1=1$ bar to $V_2=0\mathrm{.}1m^3,p_2=3$ bar. Pressure and volume are related linearly

during the process. For the gas, find the work, in kJ $.$

A closed system consisting of $0\mathrm{.}2$ lbmol of air undergoes a polytropic process from $p_1=20lb\frac{f}{i}{n}^2{?}^2,v_1=11\mathrm{.}50f\frac{t^3}{b}b$ to a

final state where $p_2=80lb\frac{f}{i}{n}^2{?}^2,v_2=3\mathrm{.}98f\frac{t^3}{l}b.$ Determine the amount of energy transfer by work, in Btu $,$ for the process.

Warm air is contained in a piston$-$cylinder assembly oriented horizontally as shown in Fig. $1.$ The air cools slowly

from an initial volume of $0\mathrm{.}003m^3$ to a final volume of $0\mathrm{.}002m^3.$ During the process, the spring exerts a force that varies

linearly from an initial value of $900$ N to a final value of zero. The atmospheric pressure is $100$ kPa $,$ and the area of the

piston face is $0\mathrm{.}018m^2.$ Friction between the piston and the cylinder wall can be neglected. For the air, determine the

work, in kJ $.$

A composite plane wall consists of a $75-$mm$-$thick layer of insulation $(x_C=0\mathrm{.}05\frac{W}{m}*K)$ and a $25-$mm$-$thick layer of

siding $(=0\mathrm{.}10\frac{W}{m}*K).$ The inner temperature of the insulation is $20C,$ the outer temperature of the siding is $-13C.$

Determine at steady state $($a$)$ the temperature at the interface of the two layers, in $C,$ and $($b$)$ the rate of heat transfer

through the wall, in W per $m_2$ of surface area.

A mass of $10$ kg undergoes a process during which there is heat transfer from the mass at a rate of $5$ kJ per kg $,$ an

elevation decrease of $50$ m $,$ and an increase in velocity from $15\frac{m}{s}$ to $30\frac{m}{s}.$ The specific internal energy decreases by $5$

$k\frac{J}{k}g$ and the acceleration of gravity is constant at $9\mathrm{.}7\frac{m}{s^2}.$ Determine the work for the process, in kJ $.$

A gas contained within a piston$-$cylinder assembly undergoes two processes, A and B $,$ between the same end states, $1$

and $2,$ where $p_1=10$ bar, $V_1=0\mathrm{.}1m^5,U_1=400kJ$ and $p_2=1$ bar, $V_2=1\mathrm{.}0m^3,U_2=200kJ$ :

Process A: Process from $1$ to $2$ during which the pressure$-$volume relation is $pV=$ constant

Process B: Constant$-$volume process from state $1$ to a pressure of $2$ bar, followed by a linear pressure$-$volume process to

state $2.$

Kinetic and potential energy effects can be ignored. For each of the processes A and B $,($a$)$ sketch the process on $p-V$

coordinates, $($b$)$ evaluate the work, in kJ $,$ and $($c$)$ evaluate the heat transfer, in kJ $.$

As shown in Fig. $2,$ a gas within a piston$-$cylinder assembly undergoes a thermodynamic cycle consisting of three

processes in series:

Process $1-2$: Compression with $U_2=U_1.$

Process $2-3$: Constant$-$volume cooling to $p_3=140$kPa,$V_3=0\mathrm{.}028m^3.$

Process $3-1$: Constant$-$pressure expansion with $W_{31}=10\mathrm{.}5kJ.$

For the cycle, $W_{\text{g}\text{e}\text{c}}=-8\mathrm{.}3kJ.$ There are no changes in kinetic or potential energy. Determine $($a$)$ the volume at state $1,$ in

$m^3,($b$)$ the work and heat transfer for process $1-2,$ each in kJ $.($c$)$ Can this be a power cycle? A refrigeration cycle? Explain.

Spring force varies linearly from $900$ N when

$V_1=0\mathrm{.}003m^3$ to zero when $V_2=0\mathrm{.}002m^3$