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Mechanical Properties Of Fluids

Question
CBSEENPH11020324

A Carnot engine operating between temperatures T1 and T2 has efficiency 1/6. When T2 is lowered by 62 K, its efficiency increases to 1/3. Then T1 and T2 are, respectively

  • 372 K and 330 K

  • 330 K and 268 K

  • 310 K and 248 K

  • 372 K and 310 K

Solution

D.

372 K and 310 K

The efficiency  is given by,
straight eta subscript 1 space equals space 1 space minus straight T subscript 2 over straight T subscript 1
rightwards double arrow space 1 over 6 space equals space 1 space minus space straight T subscript 2 over straight T subscript 1
rightwards double arrow space straight T subscript 2 over straight T subscript 1 space equals space 5 over 6
straight eta subscript 2 space equals space 1 minus fraction numerator straight T subscript 2 minus 62 over denominator straight T subscript 1 end fraction space space.... space left parenthesis straight i right parenthesis
1 third space equals space 1 minus fraction numerator straight T subscript 2 minus 62 over denominator straight T subscript 1 end fraction space... space left parenthesis ii right parenthesis
On space solving space Eqs space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis
straight T subscript 1 space equals space 372 space straight K space and space straight T subscript 2 space equals space 310 space straight K