10.2 Rescuing Gilbert Sullivan suggested one possible modification of the G-ratc
ID: 1841809 • Letter: 1
Question
10.2 Rescuing Gilbert Sullivan suggested one possible modification of the G-ratchet; here is another, which we will call the "F-ratchet." We imagine that the rod in Figure 10.10 extends far to the right, all the way into another chamber full of gas at a temperature T The rod ends with a plate in the middle of the second chamber; gas molecules bounce against this plate, giving random kicks to the rod. We further suppose that T' is greater than the temperature T of the part of the mechanism containing the 0.4 0.3 0.2 OO 0.1 3.3 3.32 3.34 3.36 3.38 3.4 3.42 1000/T, K 1 Figure 10.29: (Experimental data. Semilog plot of the frequency of flashing of firefies (arbitrary units), as a function of inverse temperature. Data from Laidler, 1972. Figure 10.30 (Schematic.) The "F-ratchet," an imagined thermal machine. Two chambers are maintained at temperatures T and T respectively; the right-hand chamber contains gas. Thermal motion in the right-hand chamber drives the shaft; its motion is rectified by the device in the left-hand chamber, perhaps lifting a weight attached to a pulley.Explanation / Answer
solution:
for a
1)here motion of wheel is not possible because plate mounted on rod are present in both side of shaft and they will cancel each other torque and shaft will not rotate in absense of ratchet .
2)if only single plate is exposed to gas then ratchet wheel will make progress in direction in which pawl is not opposing the motion of wheel due to teeth engagement with pawl and of course it will depend on kinetic energy of gases and direction of motion.
3)accordibg to kinetic theory of gases kinetic energy provided by collision is equal to
K.E.=1/2*m*C^2=1.5*R*T/N
R=gas constant, N =number of moles and hence kinetic energy of gases increse with increase in temperature due to rise in flashing frequency and on collision gives more energy to ratchet wheel as rod has plates on it and if there is any motion fixed for gas molecules then wheel will rotate in direction to gas flow direction and gives certain motion to wheel and any opposite direction will stop by pawl.
part b
1)here second law tells that total heat supplied will not converted into work completely but it gives heat away due to losses of system,in the same way if we wrap shaft in circular way and mount plate on it and any single plate is in contact with gas, then ratchet wheel will rotate in fixed direction due to pawl restriction and as per concept of entropy and conservation of energy ,entropy of gas will reduce with passing time and entropy of whhel will increase by inducing energy balance and due reduce entropy of gas ,its movement will slow down with passing time and work obtained will falls to zero and it will not voilate second law of thermodynamics.
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