KVPY SX SB Exam 05-Nov-2017 Question Paper

Question : 32 of 120

Marks: +1, -0

A thin piece of thermal conductor of constant thermal conductivity insulated on the lateral sides connects two reservoirs which are maintained at temperatures

T_1\and T_2

as shown. Assuming that the system is in steady state, which of the following plots best represents the dependence of the rate of change of entropy of the ratio of temperatures

T_1/T_2

Validate

Solution:

ds = {–Qd}/T_1+{ Qd}/T_2

{ds}/{dt}=-Q[1/T_1-1/T_2]

={-(T_1-T_2)}/R[{T_2-T_1}/{T_1T_2}]

=+({T_1^2-T^2_2}/{T_1T_2})1/R

{ds}/{dt}=(T_1/T_2-T_2/T_1)1/R

=(x-1/x)1/R

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