What would be the amount of heat absorbed in the cyclic process shown below?
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In a cyclic process, the work done is the area enclosed by the path in the pressure-volume diagram, and it equals the heat absorbed if no internal energy change occurs.
Step 1: {Understanding the Cyclic Process} For a cyclic process, the change in internal energy (\(\Delta U\)) is zero. Applying the first law of thermodynamics, \(\Delta U = q + W\), where \(q\) represents the heat absorbed and \(W\) signifies the work done. Step 2: {Work Done in a Cyclic Process} In a cyclic process, the work done corresponds to the area enclosed by the cycle on the \(p-v\) diagram. For a circular path, the work done is the area of the circle, calculated as \(W = \pi r^2\), where \(r\) is the radius of the circle. Step 3: {Calculating the Work Done} From the diagram, the radius is determined as \(r = 25 - 5 = 20\). Consequently, the work done is \(W = \pi (20)^2 = 400\pi \, {J}\). As there is no alteration in internal energy, the heat absorbed is \(q = -W\). Therefore, the heat absorbed is \(100\pi\) J.
