   Chapter 12, Problem 54P

Chapter
Section
Textbook Problem

When an aluminum bar is temporarily connected between a hot reservoir at 725 K and a cold reservoir at 310 K, 2.50 kJ of energy is transferred by heat from the hot reservoir to the cold reservoir. In this irreversible process, calculate the change in entropy of (a) the hot reservoir, (b) the cold reservoir, and (c) the Universe, neglecting any change in entropy of the aluminum rod. (d) Mathematically, why did the result for the Universe in part, (c) have to be positive?

(a)

To determine
The change in entropy of the hot reservoir.

Explanation

Given info:

The temperature of the hot reservoir is 725K .

The temperature of the cold reservoir is 310K .

The energy transferred from the hot reservoir to the cold reservoir is 2.50kJ .

The change in entropy of any reservoir is given by,

ΔS=QrT

• Qr is the energy exchanged by the reservoir
• T is the absolute temperature of the reservoir.

For a hot reservoir, the energy will be expelled by the reservoir to the system. Hence, the sign of the energy exchanged by the reservoir is negative.

Thus,

The change in entropy of the hot reservoir is,

ΔSh=|Qh|Th

• |Qh| is the energy expelled from the hot reservoir
• Th is the absolute temperature of the hot reservoir

Substitute 2

(b)

To determine
The change in entropy of the cold reservoir.

(c)

To determine
the change in entropy of the universe, neglecting any change in entropy of the aluminum rode.

(d)

To determine
mathematically, why did the result for the universe in part (c) have to be positive.

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