Heat capacity for mercury is provided both at constant
pressure volume and constant volume. If one
gram of mercury is heated at 1 atmosphere from minus 20 degrees centigrade to
100 degrees centigrade at a constant pressure of 1 atmosphere, what would be
the change in internal energy, enthalpy, entropy and volume?
Solution:
Heat capacity is a function of temperature. We have been provided with only two data
points, so we can use an average value of CP and CV as
0.331 and 0.0285 calories per g per degree Kelvin.
Internal energy change is defined as integral of CV
dT from T1 to T2.
Plugging an average value of CV,
the internal change is found to be 3.42 calories per gram.
Enthalpy energy change is equal integral of CP dT from T1 to T2.
Plugging an average value of CP,
the enthalpy change is found to be 3.936 calories per gram.
Entropy energy change is equal to integral of (CP over
T) dT from T1 to
T2. Plugging an average value
of CP, the entropy change is equal to CP ln T2 over T1. This value is equal to 0.0127 calories per
gram per degree Kelvin.
Realizing that H is defined as U plus PV, P delta V is equal
to delta H minus delta U or 0.516 calories per gram. This value is equal to 0.9288 BTU per pound. One BTU is equal to 778 ft-poundf.
So P delta V is equal to 722.6 ft-lbf
per lbm.
Pressure is equal to 1 atmosphere or 14.696 psi
or 2116.224 psf.
Now, we can find the value of delta V as 0.341 cubic foot per pound or
21.28 cubic centimeters per gram.