Question

1 kg of air at 4 bar and 150°C is contained in a system. It is expanded by a reversible process till the pressure falls to 1.01325 bar.The gas is then heated at constant pressure process until the heat content is increased by 72.5 kJ.Calculate:i) The work doneii) The pressure and temperature at the end of the constant pressure processiii) The index of expansion, if the above processes are replaced by a singlereversible polytropic process giving the same work between the sameinitial and final states.Take Cp = l kJ/kg K, Cv = 0.714 kJ/kg K.​

Answer 1

Answer:

Total work done = 85454 Nm , The index of expansion = 1.062

Explanation:

From the above question,

They have given :

1 kg of air at 4 bar and 150°C is contained in a system. It is expanded by a reversible process till the pressure falls to 1.01325 bar.The gas is then heated at constant pressure process until the heat content is increased by 72.5 kJ.

Here we have to find,

i) The work done  = 0.694 kg.

W1–2–3 = W1–2 + W2–3

Total work done = 85454 Nm

ii) The pressure and temperature at the end of the constant pressure process.

iii) The index of expansion = 1.062

Initial volume, V1 = 0.2 m3

Initial pressure,

p1 = 4 bar = 4 × 105 N/m2  

Initial temperature,

T1 = 130 + 273 = 403 K

Final pressure after adiabatic expansion,  

p2 = 1.02 bar = 1.02 × 105 N/m2  

Increase in enthalpy during constant pressure process  = 72.5 kJ.

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Answer 2

The work done in the above process is 4.8*10³J.

Given,

Mass of air= 1kg

Initial pressure = 4bar

Final pressure= 1.01325 bar

Heat =72.5kJ

To find,

Work done

Solution,

W=  2.303 nRT log(P₂/P₁)

W= 2.303*1*8.314*423 log(1/4)

W= 4.8*10³ J.

Hence, work done in the above process is 4.8*10³J.

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