Intitially, .5kg of steam with a quality of .9 at 700 kPa is held in an adiabati

Question

Intitially, .5kg of steam with a quality of .9 at 700 kPa is held in an adiabatic cylinder with a freely floating piston and a paddle wheel. The paddle wheel is then turned on for 1 minute. During this time interval, 200 KJ of work is transferred into the nitrogen from the paddle.

a) What is the initial temperature [C]?
b) What is the final temperature [C]?
c) Determine the final volume in the cylinder [m^3]? Intitially, .5kg of steam with a quality of .9 at 700 kPa is held in an adiabatic cylinder with a freely floating piston and a paddle wheel. The paddle wheel is then turned on for 1 minute. During this time interval, 200 KJ of work is transferred into the nitrogen from the paddle.

a) What is the initial temperature [C]?
b) What is the final temperature [C]?
c) Determine the final volume in the cylinder [m^3]? Intitially, .5kg of steam with a quality of .9 at 700 kPa is held in an adiabatic cylinder with a freely floating piston and a paddle wheel. The paddle wheel is then turned on for 1 minute. During this time interval, 200 KJ of work is transferred into the nitrogen from the paddle.

a) What is the initial temperature [C]?
b) What is the final temperature [C]?
c) Determine the final volume in the cylinder [m^3]?

Explanation / Answer

Given:
Mass of the steam 'm' = 0.5kg
dryness fraction 'x' = 0.9
P1 = 700kPa , V1 = 0.05m3

Work done on the system = 200kJ per minute = 3.3 kW

Adiabatic process i.e. no heat transfer ( Q = 0)

applying First Law of thermodynamics : dQ = dU + dW

dU = -dW (-ve sign indicates that the work is done on the system)

m*cp*(T2 - T1) = 3.3kW ...........eq.1

cp(specific heat of water at constant pressure)= 4.18kJ/kg.K

From staturated steam tables we get the saturation temperature of steam at 700kPa, T1=437.95K

substituting all the known values in the eq.1 we get T2 = 439.52K

for adiabatic process T.V(-1)=constant (where is 1.4)

so T1V1(-1)=T2V2(-1)

substituting all the known values u'll get V2= 0.04955m3

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