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:

The amount of heat exhausted by the heat engine can be calculated by subtracting the work done by the engine from the heat input. The engine's efficiency of 35.0% means that 35.0% of the heat input is converted into work, while the rest is exhausted as heat. For an input of 128 J, the output work is 35.0% of 128 J, which is 44.8 J. Therefore, the amount of heat exhausted is: 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.
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