The 250 litre cylinder of a steam train contains superheated steam at 300 degree
ID: 1654165 • Letter: T
Question
The 250 litre cylinder of a steam train contains superheated steam at 300 degree C and 10 atm. Assuming C_v = 7/2 R calculate (a) find numerical values for the specific heat of the steam at constant volume and aft constant pressure in Sl units. (b) the number of moles of the steam in the cylinder. (c) the amount of energy released as the steam cools down to 100 degree C if the piston is free to move, and we assume that the pressure remains constant. (d) the amount of energy released as the steam cools down to 100 degree C if the piston is held in a fixed position.Explanation / Answer
(a) Cv = (7/2)R
where R is the universla gas constant and = 8.314 J/mol-K
Hence CV = (7/2)*8.314 = 29.099 J/mol-K
Now for the specific heat at constant pressure (CP)
we know that
CP - CV = R
CP = R + CV = R + (7/2)R = 4.5R = 37.413 J/mol- K
(b) Now the no. of moles of the gas, we know that
PV = nRT
where P is pressure , V is volume , n is no. of moles , T is temperature in K
P = 10 atm = 10*1.013*105 Pa
V = 250 litre = 250*10-3 m3
T = 300 = 300+273 K
(10*1.013*105)*(250*10-3) = n*8.314*(300+273)
n = 53.16 moles
(c) We know that energy release at constant pressure is given by
Q = nCP(Tfinal - Tinitial) = 53.16*37.413*(100-300) = -397.8 kJ
-ve sign represent that energy is released
(d) At constant volume energy is given by
Q = nCV(Tfinal - Tinitial) = 53.16*29.099*(100-300) = -309.38 kJ
-ve sign represent that the energy is released.
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