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Hello; I'm having some difficulties with a thermo question of mine.
at low density water vapor conforms well to the ideal gas equation provided the temp is higher than about 320K, but the heat capacity is a function of temperature. The following formula gives the specific heat capacity at constant volume, as a function of T
cv = 1273.0 + 0.3441T + (2.833x10^-4)T^2 J/kgK
a) calculate the entropy change for 1kg of water vapour heated from 350K to 1000K at constant volume.
Here's what i did; S = (integral)dQ/T = (integral)NcvdT/T. Where N = (m/MM) = 1/0.018
I subbed cv into this equation then divided it by T
= (m/MM)(1273.0/T + 0.3441 + (2.833x10^-4)T)dT
Then integrated over T1 = 350, T2 = 1000 to get:
S = (1/0.018)(1273.0(ln(1000/350)) + 0.3441(1000-350) + ((2.833x10^-4)/2)(1000-350)^2)
however, my answer is not correct according to the back of the book. The answer is supposed to be 1.68kJ/K. Where did i go wrong?
b) Same as a) except at constant pressure.
here's what i tried;
S = (inegral)(Ncpdt)
where cp = cv + R
hwoever this also doesn't give me the correct answer.
Any help or suggestions would be greatly appreciated!
at low density water vapor conforms well to the ideal gas equation provided the temp is higher than about 320K, but the heat capacity is a function of temperature. The following formula gives the specific heat capacity at constant volume, as a function of T
cv = 1273.0 + 0.3441T + (2.833x10^-4)T^2 J/kgK
a) calculate the entropy change for 1kg of water vapour heated from 350K to 1000K at constant volume.
Here's what i did; S = (integral)dQ/T = (integral)NcvdT/T. Where N = (m/MM) = 1/0.018
I subbed cv into this equation then divided it by T
= (m/MM)(1273.0/T + 0.3441 + (2.833x10^-4)T)dT
Then integrated over T1 = 350, T2 = 1000 to get:
S = (1/0.018)(1273.0(ln(1000/350)) + 0.3441(1000-350) + ((2.833x10^-4)/2)(1000-350)^2)
however, my answer is not correct according to the back of the book. The answer is supposed to be 1.68kJ/K. Where did i go wrong?
b) Same as a) except at constant pressure.
here's what i tried;
S = (inegral)(Ncpdt)
where cp = cv + R
hwoever this also doesn't give me the correct answer.
Any help or suggestions would be greatly appreciated!