ENGR 2010 Sec 4 Thermo I- HW 4 Page 1 of1 Student Name: Student ID: (Type First
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ENGR 2010 Sec 4 Thermo I- HW 4 Page 1 of1 Student Name: Student ID: (Type First Name Last Name) Type Student ID) uao-cinder device i iniayeo Problem 4-1 (16 points). Calculate the work when the system has moving boundary The volume of 1 kg of helium in a piston-cylinder device is initially 5 m2. Now helium is compressed to 2 m3 while its pressure is maintained constant at 180 kPa. (a) (2 points) Draw the process on a P-v diagram and clearly indicate the initial state 1 and the final state 2 on your diagram and the direction of the process (use an arrow to show the direction). (b) (2 points) determine the initial and final temperatures of helium, in K, and (c) (2 points) calculate the work required to compress it, in k. (The gas constant of heli is RHe 2.0769 kJ/kg-K). wthe direction)Explanation / Answer
AnsweR--mass of helium(m)=1kg
Molecular mass of helium =4.003grams/mole
No of moles present in1 kg of ice=1000g/(4.003grams/mole)
n=1000/4.003=249.8moles
Ilitial volume(v1)=5m^3
Final volume(v2)=2m^3
Pressure(p)=180*10^3pa
T1,T2 are the initial and final temperatures
At constant pressure (v1/v2)=(T1/T2)
T1/T2=5/2
From ideal gas equation
PV1=nRT1. Here R=8.314j/mol kelvin
T1=(180*10^3*5)/(249.8*8.314)
=433.35kelvin
T2=(2/5)T1
=(0.4*433.35)
T2 =173.34kelvin
Work required to do this is=pressure *change in volume
=180*10^3*(5_2)pa m^3
=540kilojoule
=540kJ
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