Using the Energy BalanceFigure P2.70 shows a gas contained

QUESTION:

Figure P2.70 shows a gas contained in a vertical piston-cylinder assembly. A vertical shaft whose cross-sectional area is \(0.8 \mathrm{~cm}^2\) is attached to the top of the piston. The total mass of the piston and shaft is \(25 \mathrm{~kg}\). While the gas is slowly heated, the internal energy of the gas increases by \(0.1 \mathrm{~kJ}\), the potential energy of the piston-shaft combination increases by \(0.2 \mathrm{~kJ}\), and a force of \(1334 \mathrm{~N}\) is exerted on the shaft as shown in the figure. The piston and cylinder are poor conductors, and friction between them is negligible. The local atmospheric pressure is 1 bar and \(g=9.81 \mathrm{~m} / \mathrm{s}^2\). Determine,  (a) the work done by the shaft,  (b) the work done in displacing the atmosphere, and  (c) the heat transfer to the gas, all in kJ.  (d) Using calculated and given data, develop a detailed accounting of the heat transfer of energy to the gas.