KVPY 2020-21 SB SX Exam Previous Papers

Question : 27 of 120

Marks: +1, -0

An engine runs between a reservoir at temperature 200 K and a hot body which is initially at temperature of 600 K. If the hot body cools down to a temperature of 400 K in the process, then the maximum amount of work that the engine can do (while working in a cycle) is (the heat capacity of the hot body is 1 J/K)

200(1 – ln 2) J
200(1 – ln 3/2) J
200(1 + ln 3/2) J
200 J

Validate

Solution:

\η={{W}}/{{Q}_{{in}}}

\⇒{W}=\η {Q}_{{in}}

{Q}=\∫{C} {dt}

For maximum amount of work, efficiency should be maximum, means we have to assume carnot engine.

\∴\η=1-{{T}_{2}}/{{T}_{1}}=1-{200}/{{T}}

\∴{W}=\∫{n} {Q}_{{in}}=-\∫↙{600} ↖{400}(1-{200}/{{T}}) {C} {dT}

=-C[T-200 \ln T]_{600}^{400}

{W}=-{C}[-200+\ln ({3}/{2}) 200]

{C}=1

(Given)

{W}=200-200 \l{n}({3}/{2})

{W}=200(1-l{n}({3}/{2}))

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