An object of mass and specific heat capacity cools from an initial temperature to a…

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Thermodynamics · Thermodynamics

Problem

An object of mass

m

and specific heat capacity

c

cools from an initial temperature

T_1

to a final temperature

T_2

(T_1>T_2)

by coming into thermal contact with a very large heat reservoir that remains at the constant temperature

T_2

. Assume

c

is constant in this temperature range and no work is done. (i) Derive an expression for the entropy change of the object during its cooling. (ii) Derive an expression for the entropy change of the reservoir. (iii) Hence obtain the expression for the total entropy change of the universe in terms of

m

c

T_1

, and

T_2

. (iv) Using

m = 0.50\,\text{kg}

and

c = 450\,\text{J\,kg}^{-1}\,\text{K}^{-1}

, compute the total entropy change of the universe for the two separate cases: (A)

T_1 = 350\,\text{K}

T_2 = 300\,\text{K}

(B)

T_1 = 400\,\text{K}

T_2 = 300\,\text{K}

Comment on how the initial temperature difference affects entropy generation.

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