Complete Analysis of a Refrigerator

Goal Solve for the performance coefficient of a refrigerator using a fivestep process the includes:

$1.$ Making a state table.

$2.$ Making a process table.

$3.$ Calculating the totals for Work, Heat, and Internal$-$Energy$-$Change.

$4.$ Identifying the heat input $($cold reservoir$)$ and output $($hot reservoir$).$

$5.$ Calculating the performance coefficient of the refrigerator.

Problem Shown in the figure to the right is a cyclic process undergone by a refrigerator. Your refrigerator shall use $10\mathrm{.}0$ moles of helium gas $($monatomic$).$ During the process a$->$b$,$ the volume increases by a factor of $2\mathrm{.}0.$

$\backslash [$

P$\_\{$a$\}=100,000\backslash$mathrm$\{$~Pa$\}$

$\backslash ]$

Refrigerator Cycle Solution

$(1)$ Fill in the State Table $($all pressures in Pascals, all volumes in cubic meters, all temperatures in K$).$

$(2)$ Fill in the Process Table $($all entries in Joules$).$

$(3)$ Find the Totals:

$(4)$ Find the heat input $($from "cold reservoir"$)$ and the heat output $($to "hot reservoir"$)$:

$(5)$ Find the performance coefficient of the refrigerator:

Pressure

a

b

c

$\backslash$begin$\{$tabular$\}\{$ll$\}$

& Work $\backslash \backslash$

a$-$ & $17289\mathrm{.}4\backslash \backslash$

$\backslash$cline $\{2-3\}>$b & X

$\backslash$end$\{$tabular$\}$

b$-$

$\backslash (>$c $\backslash )$

c$-$

$\backslash (>$a $\backslash )$

Work $=$

Heat $\backslash (=\backslash )$

dU $=$

Q$-$hot $=$

Q $-$cold $=$

Heat

J J

J

$|\backslash (\backslash$times $\backslash$mathrm$\{$J$\}\backslash )$

$\backslash (\backslash$times $\backslash$mathrm$\{$J$\}\backslash )$

Temperature

$\backslash ([$: $\backslash$quad $1\backslash$Omega $\backslash )$ x

dU