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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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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.
Suppose that heat leaks into your kitchen refrigerator at an average rate of 300 watts. Assuming ideal operation, how much power must it draw from the wall?
In table 4.1, why does the entropy of water increase with increasing temperature, while the entropy of steam decreases with increasing temperature?
Why must you put an air conditioner in the window of a building, rather than in the middle of a room?
Use the definition of enthalpy to calculate the change in enthalpy between points 1 and 2 of the Rankine cycle, for the same numerical parameters as used in the text. Recalculate the efficiency using your corrected value of, and comment on the accuracy of the approximation.
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