Question

Three Carnot engines operate between the following temperature limits.
a) 400 and 500 K
b) 500 and 600 K
c) 400 and 600 K
Each engine extracts the same amount of energy per cycle from the high-temperature reservoir. Rank the magnitudes of the work done by the engines per cycle, greatest first. (NOTE: Use only the symbols > or = , for example b>a=c.)

Answer 1

Answer:c>a>b

Explanation:

Given

All the engine extracts same amount of heat(Q) from High-temperature reservoir

For a) 400 and 500 K

$\eta _{engine}=1-\frac{T_L}{T_H}$

$\eta _{engine}=\frac{work\ supplied}{heat\ supplied}$

$1-\frac{400}{500}=\frac{W_a}{Q}$

$W_a=\frac{Q}{5}$

For b)500 K and 600K

$1-\frac{500}{600}=\frac{W_b}{Q}$

$W-b=\frac{Q}{6}$

For c) 400 K and 600 K

$1-\frac{400}{600}=\frac{W_c}{Q}$

$W_c=\frac{2Q}{3}$

So c will give the highest amount of work

c>a>b