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Mechanical Properties Of Fluids

Question
CBSEENPH11020555

A refrigerator works between 4o C and 30o C. It is required to remove 600 calories of heat every second in order to keep the temperature of the refrigerated space constant. The power required is (Take 1 cal = 4.2 Joules)

  • 23.65 W

  • 236.5 W

  • 2365 W

  • 2.365 W

Solution

B.

236.5 W

Given,
Temperature of the source, T = 30o C = 30 + 273  = 303 K
Temperature of sink, T2 = 4o C = 4 + 273 = 277 K
We know,
space space space space space straight Q subscript 1 over straight Q subscript 2 space equals space T subscript 1 over T subscript 2

rightwards double arrow space fraction numerator Q subscript 2 space plus space W over denominator straight Q subscript 2 end fraction space equals space T subscript 1 over T subscript 2 space open curly brackets W space equals space Q subscript 1 space minus space Q subscript 2 close curly brackets
where, Q2 is the amount of heat drawn from the sink at T2,
W is the work done on the working substance,
Q1 is the amount of heat rejected to source at room temperature T1.
That is,
rightwards double arrow space WT subscript 2 space plus space straight T subscript 2 straight Q subscript 2 space equals space straight T subscript 1 straight Q subscript 2

rightwards double arrow space WT subscript 2 space equals space straight T subscript 1 straight Q subscript 2 space minus straight T subscript 2 straight Q subscript 2

rightwards double arrow space WT subscript 2 space equals space straight Q subscript 2 space left parenthesis straight T subscript 1 space minus space straight T subscript 2 right parenthesis
rightwards double arrow space straight W space equals space straight Q subscript 2 space open parentheses straight T subscript 1 over straight T subscript 2 minus 1 close parentheses
rightwards double arrow space straight W space equals space 600 space straight x space 4.2 space straight x space open parentheses 303 over 277 minus 1 close parentheses
rightwards double arrow space straight W space equals space 600 space straight x space 4.2 space straight x space open parentheses 26 over 277 close parentheses
rightwards double arrow space straight W space equals space 236. space 5 space straight J

Power space equals space fraction numerator Work space done over denominator time end fraction
space space space space space space space space space space space space equals space straight W over straight t space equals space fraction numerator 236.5 over denominator 1 end fraction
space space space space space space space space space space space space equals 236.5 space straight W