Problem 4:Caloulating Work Consider a frictioniess piston-cylinder device that c

Question

Problem 4:Caloulating Work Consider a frictioniess piston-cylinder device that contains 1 kg of helium. For helium, R-2.08 kJ/ (kg K), and c3.12J(kg K). During a process, the gas expands from a volume of 2 m2 to a volume of 4 m. Under these conditions, helium acts as an ideal gas. Show your work in answering the following 2 problems concerning work A. If the process described above occurs at a constant pressure of 100 kPa, how much work does the system produce? A. 0 kJ B. If the process described above occurs at a constant temperature of O°C, how much work does the system produce? A. Ok B. 200 k C. 394 k D. 416 kJ B. 200 kJ C. 394 kJ D. 1573 kJ

Explanation / Answer

Given,

For helium,R = 2.08 kJ/(kg.K)

Cv=3.12 kJ/(kg.K)

Vfinal = 4 m3

Vinitial= 2 m3

A. Work done at constant pressure of 100kPa = P(Vfinal-Vinitial)

= 100(4 - 2 )

= 200 k*N/m2*m3

= 200 kNm

= 200 kJ

B.Work done at constant temperature 0oC = nRT ln[Vfinal/Vinitial]

Given 1 kg of helium,so no.of moles = 249.83 but as R is mentioned in terms of kg we can keep n as 1kg

= 2.08* 273.15 * ln[4/2] kg*K*kJ/(Kg.K)

= 393.81 k J

  

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