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Chapter 1: Q.1.24 (page 17)

Calculate the total thermal energy in a gram of lead at room temperature, assuming that none of the degrees of freedom are "frozen out" (this happens to be a good assumption in this case).

Short Answer

Expert verified

The total thermal energyU=35.3J.

Step by step solution

01

Step 1. Introduction.

Each atom in lead has six degrees of freedom in terms of vibration (3kinetic and 3potential). There are no transitional degrees of freedom, and there are no rotational degrees of freedom for a single atom because the atoms are fixed in their locations in the lattice.

02

Step 2. Explanation.

Given the molar mass of lead, the number of molecules in one gram of lead is,

Hereu=1.66脳10kg27.

N=massmolar mass=1脳103kg207.2脳1.66脳1027kg=2.91脳1021

The thermal energy at T=293K

U=f2NkT=62脳2.91脳1021脳1.38脳1023脳293=35.3J

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Most popular questions from this chapter

Estimate how long it should take to bring a cup of water to boiling temperature in a typical 600-wattmicrowave oven, assuming that all the energy ends up in the water. (Assume any reasonable initial temperature for the water.) Explain why no heat is involved in this process.

Calculate the total thermal energy in a gram of lead at room temperature, assuming that none of the degrees of freedom are "frozen out" (this happens to be a good assumption in this case).

Suppose you have a gas containing hydrogen molecules and oxygen molecules, in thermal equilibrium. Which molecules are moving faster, on average? By what factor?

By applying Newton鈥檚 laws to the oscillations of a continuous medium, one can show that the speed of a sound wave is given by

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