A chemical engineer is studying the properties of liquid methanol (CH3OH). She u

Question

A chemical engineer is studying the properties of liquid methanol (CH3OH). She uses a steel cylinder with a cross sectional area of 0.0020 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 10 4N. The temperature of the system is increased from 20.0 C to 50.0C. For methanol, the coefficient of volume expansion is 1.20 x 10 -3K, the density is 791 kg/m3, and the specific heat capacity at constant pressure is cp- 2.51 x10 3 J/kg.K. You can ignore the expansion of steel. Find (a) the increase in volume of the methanol; (b) the mechanical work done by the methanol against the 3.00 x 10 4 N force (c) the amount of heat added to the methanol (d) the change in internal energy of methanol (e) Based on your results, explain whether there is any substantial difference between teh specific heat capacities Cp (at constant pressure) and Cv(at constant volume) for methanol under these conditions.

Explanation / Answer

V1 = .012 m^3

the volumetric thermal expansion coefficient can be written as   > a = dV/VdT

adT = dV/V

integrating both sides

a(T2 - T1) = ln(V2/V1)

.0012*(50 - 20) = ln(V2/.012)     (difference in temprature same in celsius and kelvin)

V2 = .012e^(.036) = 1.243 x 10^(-2) m^3

(A) thus increase in volume = V2- V1 = 4.3 x 10^(-4) m^3 (approx.)

B) distance(lenght) by which piston will move = change in volume/area = 4.3 x 10^(-4) m^3/0.0020 m^2 = .215 m

work = FdX

F =3 x 10^4 N

W = FdX = 2150*3 = 6450 J

C) weight of methanol = 791*.012 = 9.492 kg

heat added to it = mCpdT = 9.492*(2.51 x10^3)*30 = 714.7476 kJ

D) U = Q - W = 714.7476 - 6.45 = 708.298 kJ

E) Cv = 2.49 x 10^3 J/kg.K difference of order of mag. 1

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