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Chapter 12: Q42P (page 510)
Consider the exponential function . Evaluate this function for x = 1, 10,000, and 0.01.
The value of exponent function for is and the value of exponent function for is .
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Figure 12.57 shows a one-dimensional row of 5 microscopic objects each of mass , connected by forces that can be modeled by springs of stiffness 15 N/m. These objects can move only along the x axis.
(a) Using the Einstein model, calculate the approximate entropy of this system for total energy of 0, 1, 2, 3, 4, and 5 quanta. Think carefully about what the Einstein model is, and apply those concepts to this one-dimensional situation. (b) Calculate the approximate temperature of the system when the total energy is 4 quanta. (c) Calculate the approximate specific heat on a per-object basis when the total energy is 4 quanta. (d) If the temperature is raised very high, what is the approximate specific heat on a per-object basis? Give a numerical value and compare with your result in part (c).
How many different ways are there to arrange 4 quanta among 3 atoms in a solid?
Explain what it means for something to have wavelike properties; for something to have particulate properties. Electromagnetic radiation can be discussed in terms of both particles and waves. Explain the experimental verification for each of
In order to calculate the number of ways of arranging a given amount of energy in a tiny block of copper, the block is modeled as containing independent oscillators. How many atoms are in the copper block?
A box contains a uniform disk of mass M and radius R that is pivoted on a low-friction axle through its centre (Figure 12.58). A block of mass m is pressed against the disk by a spring, so that the block acts like a brake, making the disk hard to turn. The box and the spring have negligible mass. A string is wrapped around the disk (out of the way of the brake) and passes through a hole in the box. A force of constant magnitude F acts on the end of the string. The motion takes place in outer space. At time the speed of the box is , and the rotationalspeed of the disk is . At time the box has moved a distance x, and the end of the string has moved a longer distance d, as shown.
(a) At time , what is the speed of the box? (b) During this process, the brake exerts a tangential friction force of magnitude f. At time , what is the angular speed of the disk? (c) At time , assume that you know (from part b) the rotational speed of the disk. From time to time , what is the increase in thermal energy of the apparatus? (d) Suppose that the increase in thermal energy in part (c) is . The disk and brake are made of iron, and their total mass is . At time their temperature was . At time , what is their approximate temperature?
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