An ideal Carnot engine is operated as a thermodynamic pump to heat a room in the winter.The thermodynamic pump delivers thermal energy to the room at the rate of 47 kJ per second and maintains the room at a temperature of 293 K when the outside temperature is 237 K.The power requirement to run the thermodynamic pump under these operating conditions is closest to

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The power requirement for a Carnot heat pump is given by:$$P = \frac{Q_H}{T_H - T_L}$$where:* $P$ is the power in watts* $Q_H$ is the heat delivered to the room in joules per second* $T_H$ is the temperature of the room in kelvins* $T_L$ is the outside temperature in kelvinsIn this problem, we are given:* $Q_H = 47 kJ/s = 47,000 J/s$* $T_H = 293 K$* $T_L = 237 K$Substituting these values into the equation, we get:$$P = \frac{47,000 J/s}{293 K - 237 K} = 9,000 W$$Therefore, the power requirement to run the thermodynamic pump under these operating conditions is closest to 9,000 W.

An Ideal Carnot Engine Is Operated as a Thermodynamic Pump