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Chapter 3: Q78P (page 615)

.. CALC Calculate the integral in Eq. (18.30), and compare this result to as given by Eq. (18.35). (Hint:Make the change of variable and use the tabulated integral

where nis a positive integer and is a positive constant.)

Short Answer

Expert verified

By comparing the result with equation 18.33 we get the same result where the average speed of the molecule will be given by

Step by step solution

01

Determine the integral Equation and compare the result

As given

Bydifferentiatetheequation

Integrate theequation

Solve for the integral Equation

Therefore by comparing the result with (equation 18.33) we get the same result where the average speed of the molecule will be given by

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Most popular questions from this chapter

Imagine a special air filter placed in a window of a house. The tiny holes in the filter allow only air molecules moving faster than a certain speed to exit the house, and allow only air molecules moving slower than that speed to enter the house from outside. What effect would this filter have on the temperature inside the house? (It turns out that the second law of thermodynamics—which we will discuss in Chapter 20—tells us that such a wonderful air filter would be impossible to make.)

For the following processes, is the work done by the system (defined as the expanding or contracting gas) on the environment positive or negative?

(a) expansion of the burned gasoline–air mixture in the cylinder of an automobile engine

(b) opening a bottle of champagne

(c) filling a scuba tank with compressed air

(d) partial crumpling of a sealed, empty water bottle as you drive from the mountains down to sea level.

The inside of an oven is at a temperature of 200° C (392° F). You can put your hand in the oven without injury as long as you don’t touch anything. But since the air inside the oven is also at 200° C, why isn’t your hand burned just the same?

In a constant-volume process, dU = nCV dT. But in a constant-pressure process, it is not true that dU = nCp dT. Why not?

A diesel engine performs 2200 J of mechanical work and discards 4300 J of heat each cycle. (a) How much heat must be supplied to the engine in each cycle? (b) What is the thermal efficiency of the engine?
See all solutions

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