Carnot engine: A Carnot engine operates between a high temperature reservoir at and a river with water at If it absorbs of heat each cycle, how much work per cycle does it perform?
A) 1318 J
B) 2382 J
C) 1449 J
D) 2251 J

Question

Carnot engine: A Carnot engine operates between a high temperature reservoir at  and a river with water at  If it absorbs  of heat each cycle, how much work per cycle does it perform?
A) 1318 J 
B) 2382 J 
C) 1449 J 
D) 2251 J

Quizplus · Accepted Answer

The efficiency of a Carnot engine is given by the formula:

efficiency = 1 - (T_low/T_high)

where T_low and T_high are the temperatures of the cold and hot reservoirs respectively.

Now, if the engine absorbs Q amount of heat energy from the hot reservoir, then it must release an equal amount of heat energy to the cold reservoir in order to complete one cycle. Therefore, the work output of the engine is given by:

work = Q*(1 - (T_low/T_high))

In this case, we are given T_high = 11eb6b7b_2fa5_b400_b0cf_05f721a743ce_TB8274_11 and T_low = 11eb6b7b_2fa5_b401_b0cf_6bef8e39d175_TB8274_11. Substituting these values, we get:

efficiency = 1 - (11eb6b7b_2fa5_b401_b0cf_6bef8e39d175_TB8274_11/11eb6b7b_2fa5_b400_b0cf_05f721a743ce_TB8274_11) = 0.238095...

This means that the engine converts only 23.81% of the absorbed heat energy into useful work. Therefore, the work output per cycle is given by:

work = 11eb6b7b_2fa5_b402_b0cf_85b804ecc7f3_TB8274_11*(0.238095...) = 1318 J

Hence, the answer is A) 1318 J.

Carnot Engine: a Carnot Engine Operates Between a High Temperature