   Chapter 12, Problem 29P

Chapter
Section
Textbook Problem

A 5.0-kg block of aluminum is heated from 20°C to 90°C at atmospheric pressure. Find (a) the work done by the aluminum, (b) the amount of energy transferred to it by heat, and (c) the increase in its internal energy.

(a)

To determine
The work done by the aluminum.

Explanation

Given Info:

The mass of aluminum is 5kg .

Initial temperature of aluminum is 20°C .

Final temperature of aluminum is 90°C .

Formula to calculate the work done by the aluminum is,

W=P(ΔV)

• P is the pressure
• ΔV is the change in volume

The original volume of aluminum is,

V0=mρAl

• m is the mass of aluminum
• ρAl is the density of aluminum

The change in volume of aluminum is,

ΔV=βV0ΔT=(3αAl)(mρAl)(ΔT)

• β is the coefficient of volume expansion
• αAl is the coefficient of linear expansion

The work done by the aluminum is equal to the work done on the environment.

Thus,

The work done by the aluminum is,

Wenv=P(3αAl)(mρAl)(ΔT)

Substitute 1

(b)

To determine
The amount of energy transferred to aluminum by heat.

(c)

To determine
The internal energy increase of aluminum.

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