# How much heat is exhausted in each cycle and heat transfer process analysis?

1. A heat engine has an efficiency of 35.0% and receives 128 J of heat per cycle. How much heat (in Joules) does it exhaust in each cycle?

1. The heat transfer exhausts 83.2 J per cycle.

## Heat Transfer Calculation:

**128 J - 44.8 J = 83.2 J**This means that in each cycle, the heat engine exhausts 83.2 Joules of heat.

2. A refrigerator extracts 80.0 J of heat from a heat reservoir at 0.00°C. If the coefficient of performance of the refrigerator is 1.6, then how much heat (in Joules) is discharged out of the refrigerator?

2. The refrigerator discharges 200 J of heat.

## Heat Discharge Calculation:

The amount of heat discharged by the refrigerator can be calculated using the formula:**Q2 = Q1 / (Coefficient of performance - 1)**Where: Q1 = Heat extracted = 80.0 J Coefficient of performance = 1.6 Substitute the values into the formula:

**Q2 = 80.0 J / (1.6 - 1) = 200 J**Therefore, the refrigerator discharges 200 Joules of heat.

3. A heat pump uses 100 J of work to output heat at some temperature. If the heat pump withdraws 50 J of heat from the lower temperature reservoir, then what is the coefficient of performance for the heat pump?

3. The heat pump has a coefficient of performance of 1.5.

## Coefficient of Performance Calculation:

The coefficient of performance for a heat pump is calculated using the formula:**Coefficient of performance = Q2 / W**Where: Q2 = Heat delivered = 100 J (work) + 50 J (heat extracted) = 150 J W = Work done = 100 J Substitute the values into the formula:

**Coefficient of performance = 150 J / 100 J = 1.5**Therefore, the heat pump has a coefficient of performance of 1.5.