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Chapter 1: Q28P (page 1)

To prove that

Short Answer

Expert verified

The equation has been proved.

Step by step solution

01

Given data

The given values are

02

Concept of Partial Differentiation

The process of finding the partial derivative of a function is called partial differentiation. In this process, the partial derivative of a function with respect to one variable is found by keeping the other variable constant.

The formula to find the Partial derivative is given by:

03

Calculation to find the value of  CP - Cv

As it's known that and dQ = dU + PdV and PV = nRT .

The specific heat is given as

So, the value of P can be written as:

Similarly, for the value of V as follows:

04

Put the values in the gas equation PV=nRT

Substitute the value of PV in the gas equation as follows:

This is the specific heat in thermodynamics.

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Most popular questions from this chapter

Use Maclaurin series to evaluate each of the following. Although you could do them by computer, you can probably do them in your head faster than you can type them into the computer. So use these to practice quick and skillful use of basic series to make simple calculations.

d4dx4ln(1+x3)atx=0 .

Use the ratio test to show that a binomial series converges for|x|<1

ln1+x1-x

Find the values of several derivatives ofe-1/t2at t = 0. Hint:Calculate a few derivatives (as functions of t); then make the substitutionx=1/t2, and use the result of Problem 24(f) or 25.

(a) Using computer or tables (or see Chapter 7,Section 11),verify that∑n=1∞(1/n2)=π26=1.6449=,and also verify that the error in approximating the sum of the series by the first five terms is approximately 0.1813.

(b) By computer or tables verify that ∑n=1∞(1/n2)(1/2)n=π212-(1/2)(ln2)2=0.5815+

the sum of the first five terms is0.5815+

(c) Prove theorem (14.4). Hint: The error is |∑N+1∞anxn|.

Use the fact that the absolute value of a sum is less than or equal to the sum of the absolute values. Then use the fact that |an+1|≤|an|to replace all anby aN+1 , and write the appropriate inequality. Sum the geometric series to get the result.
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