Question

An output of an engine with efficiency of 20% is 215 w. it works at 8 cycles/s. how much heat is rejected each cycle?

Answer 1

To determine the heat rejected each cycle by an engine with 20% efficiency and 215 watts output at 8 cycles per second, calculate the work per cycle and use the efficiency equation to find the heat input. The difference between heat input and work done gives the heat rejected per cycle, which is 107.5 joules.

Step-by-step explanation:

Calculating Heat Rejected in a Heat Engine Cycle

The question asks how much heat is rejected each cycle by an engine with 20% efficiency and an output of 215 watts, operating at 8 cycles per second. Efficiency in the context of a heat engine is defined as the ratio of the work output (W) to the heat input (Qh). The heat rejected per cycle can be calculated using the formula:

Efficiency (e) = W/Qh and W = Qh - Qc

Given the engine's efficiency (e) and its power output (W), the heat rejected per cycle (Qc) can be found by rearranging these equations and applying the given values.

1. 
   
3. Calculate the total work done per second (power): W (per second) = 215 watts = 215 joules/second.
4. 
   
6. Determine the total work per cycle by dividing the work per second by the number of cycles per second: W (per cycle) = 215 J/s / 8 cycles/s = 26.875 J.
7. 
   
9. Find the heat input per cycle using the efficiency: Qh (per cycle) = W (per cycle) / efficiency = 26.875 J / 0.20 = 134.375 J.
10. 
    
12. Calculate the heat rejected per cycle: Qc (per cycle) = Qh - W = 134.375 J - 26.875 J = 107.5 J.

Thus, the engine rejects 107.5 joules of heat each cycle.