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NEET PHYSICSThermodynamicsMedium

Question

The temperature inside a refrigerator is t2Ct_2^\circ\text{C} and the room temperature is t1Ct_1^\circ\text{C}. The amount of heat delivered to the room for each joule of electrical energy consumed ideally will be:

A

t1t1t2\frac{t_1}{t_1-t_2}

B

t1+273t1t2\frac{t_1+273}{t_1-t_2}

C

t2+273t1+t2\frac{t_2+273}{t_1+t_2}

D

t1+t2t1+273\frac{t_1+t_2}{t_1+273}

Step-by-Step Solution

The coefficient of performance (β\beta) of a refrigerator is given by β=Q2W=T2T1T2\beta = \frac{Q_2}{W} = \frac{T_2}{T_1 - T_2}, where Q2Q_2 is the heat extracted from the refrigerator (cold reservoir), WW is the work done (electrical energy consumed), T1T_1 is the absolute temperature of the room (hot reservoir), and T2T_2 is the absolute temperature inside the refrigerator. The total heat delivered to the room is Q1=Q2+WQ_1 = Q_2 + W. We need to find the amount of heat delivered per joule of work done, which is Q1W\frac{Q_1}{W}. Q1W=Q2+WW=Q2W+1=β+1\frac{Q_1}{W} = \frac{Q_2 + W}{W} = \frac{Q_2}{W} + 1 = \beta + 1 Substituting the expression for β\beta: Q1W=T2T1T2+1=T2+T1T2T1T2=T1T1T2\frac{Q_1}{W} = \frac{T_2}{T_1 - T_2} + 1 = \frac{T_2 + T_1 - T_2}{T_1 - T_2} = \frac{T_1}{T_1 - T_2} Converting the given Celsius temperatures to Kelvin: T1=t1+273T_1 = t_1 + 273 T2=t2+273T_2 = t_2 + 273 Now, substitute the temperatures into the ratio: Q1W=t1+273(t1+273)(t2+273)=t1+273t1t2\frac{Q_1}{W} = \frac{t_1 + 273}{(t_1 + 273) - (t_2 + 273)} = \frac{t_1 + 273}{t_1 - t_2} For each joule of electrical energy consumed (W=1 JW = 1\text{ J}), the heat delivered is t1+273t1t2\frac{t_1 + 273}{t_1 - t_2}.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from Thermodynamics. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSThermodynamicstemperatureinsiderefrigeratortcirctextctemperature

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