   Chapter 12, Problem 67AP

Chapter
Section
Textbook Problem

A 1.0 × 102-kg steel support rod in a building has a length of 2.0 m at a temperature of 20.0°C. The rod supports a hanging load of 6.0 × 103 kg. Find (a) the work done on the rod as the temperature increases to 40.0°C, (b) the energy Q added to the rod (assume the specific heat of steel is the same as that for iron), and (c) the change in internal energy of the rod.

(a)

To determine
The work done on the road.

Explanation

Section1:

To determine: The change in length of the rod.

Answer: the change in length of the rod is 4.4×104m .

Explanation:

Given Info:

The length of the rod is 2m .

Initial temperature is 20.0°C .

Finial temperature is 40.0°C .

Formula to calculate the change in length of the rod is,

ΔL=αL0(ΔT)

• α is the coefficient of linear expansion
• L0 is the initial length of the rod
• ΔT is the change in temperature

Substitute 11×106(°C)1 for α , 2m for L0 and 20.0°C for ΔT to find the change in length of the rod,

ΔL=(11×106(°C)-1)(2.0m)(20°C)=4.4×104m

Thus, the change in length of the rod is 4

(b)

To determine
The energy added to the rod.

(c)

To determine
the change in internal energy of the rod.

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