One mole helium is enclosed in a cylinder with a moveable piston By placing the

Question

One mole helium is enclosed in a cylinder with a moveable piston By placing the cylinder in contact with various reservoirs and also insulating it at the proper times, the helium preforms the cycle shown in the figure below Process AB is isothermal. BC is adiabatic, CD is isobaric. and DA is isochoric. Compute the internal energy change, heat transferred, and work performed for each portion of the cycle and total amount of each of these quantities for entire cycle Assume helium to be an ideal gas and C_P=20 8 J/mole K and C_v=12.5 J/mol.K

Explanation / Answer

The total internal-energy change in any cyclic process is zero

Isothermal Expansion AB

q2 = – w1 = R T2 ln (V2 / V1) =

Adiabatic ExpansionBC

q =0

U=– w2 = – Cv (T2 – T1)

Isothermal Compression CD

internal energy change is equal to zero i.e. U = 0.

-q1 = w3 = R T1 ln (V4 / V3) …

Adiabatic Compression DA

q=0

U = w

U = w = Cv T = Cv (T2 – T1)

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