1. The following are values of heat capacity for nitrogen gas: Using the general
ID: 1048216 • Letter: 1
Question
1. The following are values of heat capacity for nitrogen gas:
Using the general formula, Cv= A+BT+ C/T2, find values for A, B, and C that fit the given data.
2. Two common properties of materials are the compressibility at a given temperature and the expansion due to heating. These properties are measured by the isothermal compressibility KT and the expansion coefficient . These coefficients are defined as KT = -1/V (V/P)T and a= 1/V (V/T)p.
Use the definition given above and the general equation Cp- Cv= 2 TV/KT to find the relation between the heat capacities at constant pressure and volume for an ideal gas.
Please provide an explanation to the answers. Thank you!
Temp (K) Cv (J/molK) 300 20.8 600 21.8 1100 24.9Explanation / Answer
1.
Cv= A+BT+ C/T2 = 20.8 = A + 300B + C/90000 ...............AT 300K (1)
Cv = 21.8 = A + 600B + C/360000 .................AT 600K(2)
Cv = 24.9 = A + 1100B + C/1210000 .................. AT 1100 K(3)
EQ2-EQ1
1 = 300B - C(1/90000 - 1/360000)
1 = 300B - 8.33333 *10^-6C
EQ3-EQ2
3.1 = 500B -1.95133*10^-6 C
B=6.668807 * 10^-3
C=1.20*10^5
PUTTING THEM IN 1 WE GET
A=17.464
2.
Cp- Cv= 2 TV/K
For an ideal gas
PV = NRT
SO (V/T)p. = NR/P
= (1/V) * NR/P = 1/T
(V/P)T =( -1/P2 )* NRT
K = - 1/V * ( -1/P2 )* NRT = 1/P
SO
Cp- Cv = (1/T2) * TVP = PV/T = R(for one mole of an ideal gas)
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