A Thermodynamic Process in a Liquid A chemical engineer is studying the properties of liquid methanol (CH3OH). She uses a steel cylinder with a cross-sectional area of 0.0200 m2 and containing 1.20 X 10-2 m3 of methanol. The cylinder is equipped with a tightly fitting piston that supports a load of 3.00 X 104 N. The temperature of the system is increased from 20.0oC to 50.0oC. For methanol, the coefficient of volume expansion is 1.20 X 10-3 K-1 , the density is 791 kg/m3, and the specific beat capacity at constant pressure is Cp = 2.51 X 103 J/kg· K You can ignore the expansion of the steel cylinder. Find
(a) The increase in volume of the methanol;
(b) The mechanical work done by the methanol against the 3.00 X 104 N force;
(c) The amount of heat added to the methanol;
(d) The change in internal energy of the methanol.
(e) Based on your results, explain whether there is any substantial difference between the specific beat capacities Cp (at constant pressure) and Cv (at constant volume) for methanol under these conditions.