Question

imagine an ideal (carnot) refrigerator that keeps soda bottles chilled to a temperature of about 280 k . the refrigerator is located in a hot room with a temperature of about 300 k . because of the imperfect insulation, 5.00 j of heat is absorbed by the refrigerator each hour. how much electrical energy e must be used by the refrigerator to maintain the temperature of 280 k inside for one hour? express your answer in joules to three significant figures.

Answer 1

To maintain a temperature of 280 K inside the refrigerator for one hour, approximately 0.357 J of electrical energy is required.

Step-by-step explanation:

The electrical energy required by the refrigerator can be calculated using the equation:

e = Qin/COP

Where:

• e is the electrical energy
• Qin is the heat absorbed by the refrigerator (in this case, 5.00 J)
• COP is the coefficient of performance of the refrigerator

To find the COP, we can use the Carnot efficiency formula:

COP = T1 / (T2 - T1)

Where:

• T1 is the temperature inside the refrigerator (280 K)
• T2 is the temperature outside the refrigerator (300 K)

Plug in the values and calculate:

COP = 280 K / (300 K - 280 K) = 14

Then, use the COP to calculate the electrical energy:

e = 5.00 J / 14 = 0.357 J (to three significant figures)

Answer 2

To maintain a temperature of 280 K inside the Carnot refrigerator, approximately 0.357 J of electrical energy is required for one hour.

Step-by-step explanation:

To calculate the amount of electrical energy needed by the Carnot refrigerator to maintain a temperature of 280 K inside for one hour, we can use the formula: e = Q / COP where Q is the amount of heat absorbed by the refrigerator and COP is the coefficient of performance of the refrigerator.

Given that 5.00 J of heat is absorbed and the refrigerator is ideal (Carnot), we can calculate the COP using the formula: COP = Tc / (Th - Tc) where Tc is the absolute temperature inside the refrigerator (280 K) and Th is the absolute temperature of the hot room (300 K).

Plugging in the values, we get: COP = 280 K / (300 K - 280 K) = 14.00.

Finally, we can calculate the electrical energy used using the formula: e = 5.00 J / 14.00 = 0.357 J (rounded to three significant figures).