Air is contained in a vertical piston-cylinder assembly with an electrical resis

Question

Air is contained in a vertical piston-cylinder assembly with an electrical resistor. the atmosphere exerts a pressure of 14.7lbf/sq inch on the top of the piston which has a mass of 100lb and a face area of 1 sq foot. electrical current passes through the resistor, and the volume of the air slowly increases by 1.6 cubic ft while the pressure remains constant. the mass of the air is 0.6 lb and its specific internal energy increases by 18 Btu/lb. the air and piston are at rest initially and finally. the piston cylinder material is a good insulator. friction between the piston and cylinder wall can be ignored, and the local acceleration of gravity is 32 ft/sq second. determine the heat transfer from the resistor to the air is BTU for a system consisting of only air.

Explanation / Answer

Here   heat transfers from system to surroundings at constanty pressure   .this process is called isobaric process .       pressure exexted on the piston is  P = 14.7 lb / sq inch                                                           = 14.7*6.895*10^ 3 Pa          change in volume   ?V = 1.6 / 35.31   m ^ 3       Specific internal energy   U = 18 BTU / lb                                                 = 1.005*10^ 3 J / lb   = 1.005 *10^ 3 ( ft lb / lb )                                               = 1.005*1.356*10^ 3 J    work done by the gas                    W =   P ?V =   ( 14.7*6.895*10^ 3 )( 1.6/35.31 ) = 4.59 kJ          heat transfr from resistance to the air is                     Q = W + U    =   ...........   J      

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