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Chapter 1: 1.18. (page 13)

Calculate the rms speed of a nitrogen molecule at a room temperature?

Short Answer

Expert verified

The rms speed of a nitrogen molecule at room temperature is 16.34 m/s

Step by step solution

01

Arriving at rms speed by substituting the data ,

Since we are recalculating for Nitrogen molecule the molar mass of N2=28

Substituting all the values ,

Vrms=3×8.314×30028

Vrms=16.34m/s

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Most popular questions from this chapter

Measured heat capacities of solids and liquids are almost always at constant pressure, not constant volume. To see why, estimate the pressure needed to keep Vfixed as Tincreases, as follows.

(a) First imagine slightly increasing the temperature of a material at constant pressure. Write the change in volume,dV1, in terms of dTand the thermal expansion coefficient βintroduced in Problem 1.7.

(b) Now imagine slightly compressing the material, holding its temperature fixed. Write the change in volume for this process, dV2, in terms of dPand the isothermal compressibility κT, defined as

κT≡−1V∂V∂PT

(c) Finally, imagine that you compress the material just enough in part (b) to offset the expansion in part (a). Then the ratio of dPtodTis equal to (∂P/∂T)V, since there is no net change in volume. Express this partial derivative in terms of βandκT. Then express it more abstractly in terms of the partial derivatives used to define βandκT. For the second expression you should obtain

∂P∂TV=−(∂V/∂T)P(∂V/∂P)T

This result is actually a purely mathematical relation, true for any three quantities that are related in such a way that any two determine the third.

(d) Compute β,κT,and(∂P/∂T)Vfor an ideal gas, and check that the three expressions satisfy the identity you found in part (c).

(e) For water at 25∘C,β=2.57×10−4K−1andκT=4.52×10−10Pa−1. Suppose you increase the temperature of some water from 20∘Cto30∘C. How much pressure must you apply to prevent it from expanding? Repeat the calculation for mercury, for which (at25∘C)β=1.81×10−4K−1andκT=4.04×10−11Pa−1

Given the choice, would you rather measure the heat capacities of these substances at constant vor at constant p?

The Fahrenheit temperature scale is defined so that ice melts at 320 F and water boils at 2120 F.

(a) Derive the formula for converting from Fahrenheit to Celsius and back

(b) What is absolute zero on the Fahrenheit scale?

Problem 1.36. In the course of pumping up a bicycle tire, a liter of air at atmospheric pressure is compressed adiabatically to a pressure of 7 atm. (Air is mostly diatomic nitrogen and oxygen.)

(a) What is the final volume of this air after compression?

(b) How much work is done in compressing the air?

(c) If the temperature of the air is initially300K , what is the temperature after compression?

At about what pressure would the mean free path of an air molecule at room temperature equal 10cm, the size of a typical laboratory apparatus?

Imagine some helium in a cylinder with an initial volume of 1 liter and an initial pressure of 1 atm. Somehow the helium is made to expand to a final volume of 3 liters, in such a way that its pressure rises in direct proportion to its volume.

  1. Sketch a graph of pressure vs. volume for this process.
  2. Calculate the work done on the gas during this process, assuming that there are no “other” types of work being done.
  3. Calculate the change in the helium’s energy content during this process.
  4. Calculate the amount of heat added to or removed from the helium during this process.
  5. Describe what you might do to cause the pressure to rise as the helium expands.
See all solutions

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