Note: We will call an independent way for a system to have thermal energy a “mod

Question

Note: We will call an independent way for a system to have thermal energy a “mode.” It is sometimes also referred to in other physics textbooks as a “degree of freedom.”

3.2.6-5) What is the relationship between temperature (T) and the amount of thermal energy per mode?

3.2.6-6) For each of the following pairs, circle the system that has the greater thermal energy. If their thermal energy is the same, circle both.

a) 1 mole of a monatomic solid at 250 K or 1 mole of a monatomic solid at 300 K

b) 2 moles of a monatomic solid at 273 K or 1 mole of a monatomic solid at 273 K

c) 1 mole of a monatomic gas at 290 K or 1 mole of a monatomic solid at 290 K

d) 1 mole of a monatomic gas at 300 K or 6.02 x 1023 atoms of a monatomic gas at 300 K

e) 1 mole of a diatomic gas at 290 K or 1 mole of a monatomic gas 290 K

Please as detail as possible for solution and why you chose one over the other so I can learn. Thank you in advance. Illustrations are always a plus!

Explanation / Answer

PartA;

Internal energy per "mode" = 0.5 nRT ; n= no. of moles, R = gas constant , T = temp. in K

Part B:

ANswers

A:

1 mole of a monatomic solid at 300 K. bECAUSE Internal energy is directly depending on Temp.

B;

2 moles of a monatomic solid at 273 K. Because U= nfRT/2 ; n = no. of moles

C:

1 mole of a monatomic gas at 290 K .Because U = nfRT/2 ; n = degree of freedome , solids have less degree of freedome than gases

D:

bOTH HAVE SAME Beacsue both quantity represents same amount of same gas (which is 1 mole of gas)

E:

1 mole of a diatomic gas at 290 K because U= nfRT/2 ; f= degree of freedome , Higher the atomicity more will be degree of freedome

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