P

V

dw P V= −∫The system (the engine) does work.

0 tot totU q wΔ = = +

tot totq w= −wtot < 0

qtot > 0

h ctotq q q= + h c 0q q+ >

Heat flows into the system (qh > 0) to

maintain constant temp

Heat flows out of the system (qc < 0) to

maintain constant temp

h cq q>

Carnot Cycle

Carnot Cycle

+

Carnot Cycle

CarnotEngine

A gas that is undergoing the four stages of the Carnot cycle

qh

qc

wtot

( )h ctotw q q= − +

This will be a neg. number. Which means the engine did work (that’s a good thing.)

How much work is done if 50 kJ of heat flows into the engine and -40 kJ are returned to the cold source ?

Engine Efficiency Define engine efficiency as the ratio of the total work done divided by the heat input .

carn engh

tot. .

wq

ε =

h c

h cq qT T

= −h ccarn eng

h. .

q qq

ε +=

ccarn eng

h

1. .TT

ε = −

Carnot Cycle

-

Carnot RefrigeratorsA Carnot fridge is a Carnot Engine in reverse.

dw P V= −∫The system (the fridge)

requires work input. (wtot > 0)

Carnot Cycle

This makes sense, a refrigerator must remove heat from an already cold source and place it in a hot sink (the room).

Heat (qc) flows into the system (qc > 0) to maintain constant temp .

Heat (qh) flows out of the system (qh < 0) to maintain constant temp .

P

V

qc

qh

The Fridge

The Room

wtot CarnotFridge

A gas that is undergoing the four stages of the Carnot cycle in reverse.

tot totq w= −

But now wtot > 0, so…

totq 0<

h c 0q q+ <

h cq q>

qc > 0

qh < 0

More heat is dumped into the room than is removed from the fridge !

Carnot Cycle

Carnot Refrigerator Efficiencyc

carn fri. .tot

qw

η =

h c

h cq qT T

= −c

carn frih c

. .q

q qη =

+

ccarn fri. .

h c

TT T

η =−

A household refrigerator’s freezer compartment works at 255 K. Assuming that the room’s temperature is 294 K, what is the maximum efficiency ? How much work is required to remove 65 J of heat from the freezer ?

Carnot Cycle