An Introduction to Thermal Physics
An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter 7.5, Problem 63P
To determine

The expression for thermal energy of two dimensional solid and evaluate approximately for very low and very high temperatures. The expression for specific heat.

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Heat flows through a pipe wall, with a radius in Ri and outer radius Ro. The length of the pipe is L. The thermal conductivity of the pipe material is proportional to the temperature squared in the form: k=aT²+b a. Derive the equation for the pipe wall temperature profile, b. Calculate the heat loss through the pipe wall.
A hollow cylinder has length L, inner radius R, and thickness d, and the temperatures at the inner and outer surfaces are Tn and Ti, respectively. The thermal conductivity of the material of which the cylinder is made is k. Derive an equation for the rate of heat transfer P through the walls of the cylinder. Simplify this equation assuming that the thickness of the cylinder d is much smaller than the its inner radius R.
An unknown liquid has density ρ and coefficient of volume expansion β. A quantity of heat Q is added to a volume V of the liquid, and the volume of the liquid increases by an amount ΔV. There is no phase change. In terms of these quantities, what is the specific heat capacity c of the liquid? Express your answer in terms of the variables ρ, β, Q, V, and ΔV, if needed.
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