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Chapter 4: 4.8 (page 129)
Can you cool off your kitchen by leaving the refrigerator door open? Explain.
No, rather it will heat the kitchen.
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It has been proposed to use the thermal gradient of the ocean to drive a heat engine. Suppose that at a certain location the water temperature is at the ocean surface and at the ocean floor.
(a) What is the maximum possible efficiency of an engine operating between these two temperatures?
(b) If the engine is to produce of electrical power, what minimum volume of water must be processed (to suck out the heat) in every second?
Liquid HFC-134a at its boiling point at 12 bars pressure is throttled to 1 bar pressure. What is the final temperature? What fraction of the liquid vaporizes?
Table 4.3. Properties of the refrigerant HFC-134a under saturated conditions (at its boiling point for each pressure). All values are for of fluid, and are measured relative to an arbitrarily chosen reference state, the saturated liquid at c. Excerpted from Moran and Shapiro (1995).
The amount of work done by each stroke of an automobile engine is controlled by the amount of fuel injected into the cylinder: the more fuel, the higher the temperature and pressure at points 3 and 4 in the cycle. But according to equation 4.10, the efficiency of the cycle depends only on the compression ratio (which is always the same for any particular engine), not on the amount of fuel consumed. Do you think this conclusion still holds when various other effects such as friction are taken into account? Would you expect a real engine to be most efficient when operating at high power or at low power? Explain.
The magnetic field created by a dipole has a strength of approximately , where r is the distance from the dipole and is the "permeability of free space," equal to exactly in SI units. (In the formula I'm neglecting the variation of field strength with angle, which is at most a factor of 2.) Consider a paramagnetic salt like iron ammonium alum, in which the magnetic moment of each dipole is approximately one Bohr magneton , with the dipoles separated by a distance of . Assume that the dipoles interact only via ordinary magnetic forces.
(a) Estimate the strength of the magnetic field at the location of a dipole, due to its neighboring dipoles. This is the effective field strength even when there is no externally applied field.
(b) If a magnetic cooling experiment using this material begins with an external field strength of , by about what factor will the temperature decrease when the external field is turned off?
(c) Estimate the temperature at which the entropy of this material rises most steeply as a function of temperature, in the absence of an externally applied field.
(d) If the final temperature in a cooling experiment is significantly less than the temperature you found in part (c), the material ends up in a state where is very small and therefore its heat capacity is very small. Explain why it would be impractical to try to reach such a low temperature with this material.
A small scale steam engine might operate between the temperatures and , with a maximum steam pressure of bars. Calculate the efficiency of a Rankine cycle with these parameters.
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