2 Air is enclosed in a piston cylinder with a paddle wheel I

2. Air is enclosed in a piston cylinder with a paddle wheel. Initially, the air is at 400kPa and 17 c. he paddle wheel now is turned on and 75k /kg of work is added. Heat is added to keep the temperature constant and the volume triples. What amount ofheat is required to do t (J/kg).

Solution

In paddle work all will go to internal energy

W = U= m Cv dT

75 = 1* 0.718* dT

T2 =104.45 + 290 =394.45 K

V2 = R T/ P =0.287*394.45/400 =0.283 m3

heat added = wor done in isothermal process = P2 V2 ln(V3/V2) = 400*0.283* ln 3 = 124.37 kj/kg