Final answer:
To calculate the efficiency of a Carnot cycle with given parameters, the temperature of the source is converted to Kelvin and the formula for work done (W = S * (Tₖ - Tₗ)) is used to find the sink temperature. The efficiency is then calculated using the formula Η = 1 - (Tₗ / Tₖ), resulting in an efficiency of 66.68% and a sink temperature of 200.15 K.
Step-by-step explanation:
The question involves calculating the efficiency of a Carnot cycle which receives heat at 327°C and causes an entropy increase of 5 kJ/kg K while delivering 2000 kJ/kg of work. To determine the efficiency of the cycle, we use the following formula:
Η = 1 - Τₗ/Τₖ
Where Τₗ is the temperature of the sink (in Kelvin), and Τₖ is the temperature of the source (also in Kelvin). First, convert the source temperature from Celsius to Kelvin:
Τₖ = 327°C + 273.15 = 600.15 K
The work done by the engine is the product of the entropy increase and the temperature difference between the source and the sink:
W = S * (Τₖ - Τₗ)
Given W = 2000 kJ/kg, S = 5 kJ/kg K, and Τₖ = 600.15 K, we can now solve for Τₗ:
2000 = 5 * (600.15 - Τₗ)
400 = 600.15 - Τₗ
Τₗ = 600.15 - 400 K = 200.15 K
Now, we can calculate the efficiency using the formula:
Η = 1 - (200.15 / 600.15)
Η = 0.6668 or 66.68%
The efficiency of the cycle is 66.68%, and the temperature of the sink is 200.15 K.