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} In a cyclic process, the internal energy change (\(\Delta U\)) is zero. According to the first law of thermodynamics: \[ \Delta U = q + W \] where \(q\) is heat absorbed and \(W\) is the work done. Step 2: {Work Done in a Cyclic Process} The work done in a cyclic process is equal to the area enclosed by the cycle in the \(p-v\) diagram. For a process with a circular path, the work done is the area of the circle, which is given by: \[ W = \pi r^2 \] where \(r\) is the radius of the circle. Step 3: {Calculating the Work Done} From the diagram, the radius \(r = 25 - 5 = 20\). Therefore: \[ W = \pi (20)^2 = 400\pi \, {J} \] Since there is no change in internal energy, the heat absorbed \(q = -W\). Thus, the heat absorbed is \(100\pi\) J.
