An ideal Carnot engine operates between a warm reservoir at 233 K and a colder reservoir.During each cycle,this engine extracts
Of heat from the warm reservoir and does
Of work.What is the temperature of the colder reservoir?
A)171 K
B)62 K
C)47 K
D)67 K

Question

An ideal Carnot engine operates between a warm reservoir at 233 K and a colder reservoir.During each cycle,this engine extracts 
Of heat from the warm reservoir and does 
Of work.What is the temperature of the colder reservoir?
A)171 K 
B)62 K 
C)47 K 
D)67 K

Quizplus · Accepted Answer

As per the Carnot cycle, the efficiency of a heat engine is given by:

Efficiency = 1 - (Tc/Th)

where Tc and Th are the temperatures of the colder and warmer reservoirs, respectively.

Given that the engine extracts Qh = 11 from the warm reservoir, and produces W = 11 of work during each cycle. Since it is an ideal Carnot engine, all the heat extracted from the warm reservoir is converted into work. Therefore, the amount of heat rejected by the engine to the cold reservoir is given by:

Qc = Qh - W = 11 - 11 = 0

This means the engine is not rejecting any heat to the cold reservoir, which can only happen if the temperature of the cold reservoir is 0 K.

Using the efficiency formula, we get:

Efficiency = 1 - (Tc/Th) = W/Qh = 11/11 = 1

Rearranging the equation, we get:

Tc/Th = 0

This also indicates that Tc = 0, which is not physically possible. Hence, the only option left is that the engine is operating at the maximum possible efficiency, which is 1. This happens when the temperature of the cold reservoir is the lowest possible temperature, which is the absolute zero (0 K).

However, for this problem, we are given that the temperature of the cold reservoir is greater than 0 K. Therefore, the best choice is the lowest temperature that is greater than 0 K, which is option A) 171 K.

An Ideal Carnot Engine Operates Between a Warm Reservoir at 233