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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

Total thermal energy is 35.3 J.

Step by step solution

01

Given information

Temperature T = 298 K

Number of degree of freedom f= 6 (3 kinetic + 3 potential)

02

Explanation

Total thermal energy is calculated for system is

Uthermal=Nf12kT......................(1)

Where

N = number of molecules

k = Boltzmann constants

T = temperature

f = number of degree of freedom

lead has degree of freedom of f= 6

molecular mass of lead is 207.2 u

we can calculate number of molecules as

N=massmolecular mass

Here mass is 1 gram =1 x 103kg

molecular mass is 207.2 u = 207.2 x 1.6 x 10-27 kg

Substitute the values, we get

N=1脳10-3k207.2脳1.6脳10-27kgN=2.91脳1021

Now substitute the values in equation (1) to get thermal energy

Uthermal=62脳(2.91脳1021)脳(1.38脳10-23JK-1)脳(298K)Uthermal=35.3J

Total thermal energy is 35.3 J.

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