Tag: Solutions

Problem 3.25 In Problem 2.18 you showed that the multiplicity of an Einstein solid containing N oscillators and q energy units is approximately (a) Starting with this formula, find an expression for the entropy of an Einstein solid as a function of and Explain why the factors omitted from the formula have no effect on…

Problem 3.23 Show that the entropy of a two-state paramagnet, expressed as a function of temperature, is , where Check that this formula has the expected behavior as and Solution: Problem 3.23 Solution (Download)

Problem 3.19 Fill in the missing algebraic steps to derive equations 3.30, 3.31, and 3.33. Solution: Problem 3.19 Solution (Download)

Problem 3.18 Use a computer to reproduce Table 3.2 and the associated graphs of entropy, temperature, heat capacity, and magnetization. (The graphs in this section are actually drawn from the analytic formulas derived below, so your numerical graphs won’t be quite as smooth.) Solution: Problem 3.18 Solution (Download)

Problem 3.14 Experimental measurements of the heat capacity of aluminum at low temperatures (below about 50 K) can be fit to the formula where is the heat capacity of one mole of aluminum, and the constants and are approximately and From this data, find a formula for the entropy of a mole of aluminum as…

Problem 3.10 An ice cube (mass 30 g) at 0°C is left sitting on the kitchen table, where it gradually melts. The temperature in the kitchen is 25°C.(a) Calculate the change in the entropy of the ice cube as it melts into water at 0°C. (Don’t worry about the fact that the volume changes somewhat.)(b)…

Problem 3.9 In solid carbon monoxide, each CO molecule has two possible orientations: CO or OC. Assuming that these orientations are completely random (not quite true but close), calculate the residual entropy of a mole of carbon monoxide. Solution: Problem 3.9 Solution (Download)

Problem 3.7 Use the result of Problem 2.42 to calculate the temperature of a black hole, in terms of its mass (The energy is .) Evaluate the resulting expression for a one-solar-mass black hole. Also sketch the entropy as a function of energy, and discuss the implications of the shape of the graph. Solution: Problem…

Problem 3.5 Starting with the result of Problem 2.17, find a formula for the temperature of an Einstein solid in the limit Solve for the energy as a function of temperature to obtain (where is the size of an energy unit). Solution: Problem 3.5 Solution (Download)

Problem 3.1 Use Table 3.1 to compute the temperatures of solid and solid when Then compute both temperatures when Express your answers in terms of and then in kelvins assuming that Solution: Problem 3.1 Solution (Download)