PX154 - E2 - heat engine cycles and the pV diagram

cyclic processes

from $A \to X$ , engine does work:
- pushes out the piston
- heat input
but from $B \to Y$ , work is done on the system:
- the piston needs to be pushed back in
- heat output
process is useful since $W = \int p . d V = p Δ V$
- $W$ is larger for $A \to X$ than $B \to Y$
- useful work is done
around one complete cycle:
$Δ U = 0$
$W \neq 0$
$Q \neq 0$

heat engine depictions

summary

$Q_{C} \neq 0 :$ always
$W = Q_{H} + Q_{C}$
$Q_{H} + v e$
$Q_{C} - v e$
the efficiency is defined as the ratio of what we want to obtain to what we have to put in:

ϵ = \frac{W}{Q_{H}} = \frac{Q_{H} + Q_{C}}{Q_{H}}

$ϵ = 1 (100 %)$ only if $Q_{C} = 0$ , which never happens
eg: otto cycle (petrol engine), diesel cycle [YF fig 20.5-20.7], stirling cycle, carnot cycle

fridge and heat pumps

[YF 20.4]

cycle is ran in reverse and work, $W$ , is put into the system
efficiency, known as the coefficient of performance $C O P$ or $k$
for fridge:

k_{f r} = \frac{| Q_{C} |}{| W |} = \frac{| Q_{C} |}{| Q_{H} | - | Q_{C} |} $ $ [Y F e q n 20.9]! [P a s t e d i m a g e 20231101104054. p n g] (/ i m g / u s e r / p i c s / P a s t e d - h e a t p u m p : $ $ k_{h p} = \frac{| Q_{H} |}{| W |} = \frac{| Q_{H} |}{| Q_{H} | - | Q_{C} |}

eg: rankine cycle (fridge) , stirling cycle in reverse, gifford-macmahon cycle (cryocooling), pulse tube