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Q. 5.21

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An Introduction to Thermal Physics
Found in: Page 163
An Introduction to Thermal Physics

An Introduction to Thermal Physics

Book edition 1st
Author(s) Daniel V. Schroeder
Pages 356 pages
ISBN 9780201380279

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Short Answer

Is heat capacity (C) extensive or intensive? What about specific heat (c) ? Explain briefly.

Heat capacity is an extensive property

Specific heat is an intensive property.

See the step by step solution

Step by Step Solution

Step1: Given Information

Heat Capacity C and

Specific Heat c.

Step2: Explanation

Explanation

On the basis of physical properties of matter, it can be classified into two parts1. Intensive property: It does not depend on the quantity which means the intensive property does not vary when the mass changes.2. Extensive property: It depends on the quantity of matter which means the extensive property varies when the mass changes.Specific heat capacity is an intensive property. Specific heat capacity is given by

c=Cm

Where c is specific heat capacity, C is the heat capacity, m is the mass.

Here both C and m are extensive properties.The ratio of two extensive property is intensive property.This means Heat capacity is an extensive property.The amount of heat capacity is given byCv=dUdTWhere, U is the internal energy and T is the temperature.U is an extensive property and T is an intensive property.The ratio of extensive to intensive results in extensive property.

Most popular questions for Physics Textbooks

In this problem you will derive approximate formulas for the shapes of the phase boundary curves in diagrams such as Figures 5.31 and 5.32, assuming that both phases behave as ideal mixtures. For definiteness, suppose that the phases are liquid and gas.

(a) Show that in an ideal mixture of A and B, the chemical potential of species A can be written μA=μA°+kTln(1-x)where A is the chemical potential of pure A (at the same temperature and pressure) and x=NB/NA+NB. Derive a similar formula for the chemical potential of species B. Note that both formulas can be written for either the liquid phase or the gas phase.

(b) At any given temperature T, let x1 and xg be the compositions of the liquid and gas phases that are in equilibrium with each other. By setting the appropriate chemical potentials equal to each other, show that x1 and xg obey the equations =1-xl1-xg=eΔGA°/RT and xlxg=eΔGB°/RT and where ΔG° represents the change in G for the pure substance undergoing the phase change at temperature T.

(c) Over a limited range of temperatures, we can often assume that the main temperature dependence of ΔG°=ΔH°-TΔS° comes from the explicit T; both ΔH° and ΔS° are approximately constant. With this simplification, rewrite the results of part (b) entirely in terms of ΔHA°,ΔHB° TA, and TB (eliminating ΔG and ΔS). Solve for x1 and xg as functions of T.

(d) Plot your results for the nitrogen-oxygen system. The latent heats of the pure substances areΔHN2°=5570 J/mol and ΔHO2°=6820 J/mol. Compare to the experimental diagram, Figure 5.31.

(e) Show that you can account for the shape of Figure 5.32 with suitably chosen ΔH° values. What are those values?

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