A heat engine, X, operates between a reservoir at 1000˚C and a body at 600˚C. Heat transfer to the heat engine is 1000 kJ and work output is 220 kJ. Another Engine, Y, operates between, the body at 600˚C and the atmosphere at 27˚C. Heat rejected to the atmosphere is 400 kJ. The body of 600˚C maintains its temperature steady and has interactions only with the two engines X & Y. Calculate the work output and thermal efficiency of the engine Y
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To calculate the work output and thermal efficiency of engine Y, we first need to determine the heat input to engine Y.
The first step is to find the heat transfer between the body and engine Y, which is the same as the heat transfer between engine X and the body because the body maintains its temperature. From the information provided, we know that the heat transfer to engine X is 1000 kJ. Therefore, the heat transfer from the body to engine Y is also 1000 kJ.
Now, we can calculate the heat rejected by engine Y to the atmosphere. We are given that the heat rejected to the atmosphere is 400 kJ.
Using the principle of energy conservation, we know that the heat input to engine Y equals the heat output plus the work output. Therefore, the heat input to engine Y is 1000 kJ + 400 kJ (heat rejected to the atmosphere) + work output.
Given that the work output is unknown, let's denote it as W. Therefore, the heat input to engine Y is 1400 kJ + W.
Now, we can calculate the thermal efficiency of engine Y using the formula:
Thermal Efficiency = (Work Output / Heat Input) x 100%
Since we are given the values in kJ, we don't need to convert units for this calculation.
Thermal Efficiency = (W / (1400 kJ + W)) x 100%
Now, you can calculate the work output and thermal efficiency of engine Y by inserting the known values into the formula.