An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter 1.2, Problem 20P
To determine
The root mean square speed of each type of molecule of
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An Introduction to Thermal Physics
Ch. 1.1 - Prob. 1PCh. 1.1 - The Rankine temperature scale (abbreviatedR) uses...Ch. 1.1 - Prob. 3PCh. 1.1 - Does it ever make sense to say that one object is...Ch. 1.1 - Prob. 5PCh. 1.1 - Give an example to illustrate why you cannot...Ch. 1.1 - Prob. 7PCh. 1.1 - For a solid, we also define the linear thermal...Ch. 1.2 - What is the volume of one mole of air, at room...Ch. 1.2 - Energy in Thermal Physics Estimate the number of...
Ch. 1.2 - Rooms A and B are the same size, and are connected...Ch. 1.2 - Calculate the average volume per molecule for an...Ch. 1.2 - A mole is approximately the number of protons in a...Ch. 1.2 - Calculate the mass of a mole of dry air, which is...Ch. 1.2 - Estimate the average temperature of the air inside...Ch. 1.2 - Prob. 16PCh. 1.2 - Prob. 17PCh. 1.2 - Prob. 18PCh. 1.2 - Suppose you have a gas containing hydrogen...Ch. 1.2 - Prob. 20PCh. 1.2 - During a hailstorm, hailstones with an average...Ch. 1.2 - Prob. 22PCh. 1.3 - Calculate the total thermal energy in a liter of...Ch. 1.3 - Calculate the total thermal energy in a gram of...Ch. 1.3 - List all the degrees of freedom, or as many as you...Ch. 1.4 - A battery is connected in series to a resistor,...Ch. 1.4 - Give an example of a process in which no heat is...Ch. 1.4 - Estimate how long it should take to bring a cup of...Ch. 1.4 - A cup containing 200 g of water is sitting on your...Ch. 1.4 - Put a few spoonfuls of water into a bottle with a...Ch. 1.5 - Imagine some helium in cylinder with an initial...Ch. 1.5 - Prob. 32PCh. 1.5 - An ideal gas is made to undergo the cyclic process...Ch. 1.5 - An ideal diatomic gas, in a cylinder with a...Ch. 1.5 - Prob. 35PCh. 1.5 - In the course of pumping up a bicycle tire, a...Ch. 1.5 - Prob. 37PCh. 1.5 - Two identical bubbles of gas form at the bottom of...Ch. 1.5 - By applying Newtons laws to the oscillations of a...Ch. 1.5 - In problem 1.16 you calculated the pressure of...Ch. 1.6 - To measure the heat capacity of an object, all you...Ch. 1.6 - The specific heat capacity of Albertsons Rotini...Ch. 1.6 - Calculate the heat capacity of liquid water per...Ch. 1.6 - Prob. 44PCh. 1.6 - Prob. 45PCh. 1.6 - Measured heat capacities of solids and liquids are...Ch. 1.6 - Your 200-g cup of tea is boiling-hot. About how...Ch. 1.6 - When spring finally arrives in the mountains, the...Ch. 1.6 - Prob. 49PCh. 1.6 - Consider the combustion of one mole of methane...Ch. 1.6 - Use the data at the back of this book to determine...Ch. 1.6 - The enthalpy of combustion of a gallon (3.8...Ch. 1.6 - Look up the enthalpy of formation of atomic...Ch. 1.6 - Prob. 54PCh. 1.6 - Heat capacities are normally positive, but there...Ch. 1.7 - Calculate the rate of heat conduction through a...Ch. 1.7 - Home owners and builders discuss thermal...Ch. 1.7 - According to a standard reference table, the R...Ch. 1.7 - Make a rough estimate of the total rate or...Ch. 1.7 - A frying pan is quickly heated on the stovetop to...Ch. 1.7 - Geologists measure conductive heat flow out of the...Ch. 1.7 - Consider a uniform rod of material whose...Ch. 1.7 - Prob. 63PCh. 1.7 - Make a rough estimate of the thermal conductivity...Ch. 1.7 - Prob. 65PCh. 1.7 - In analogy with the thermal conductivity, derive...Ch. 1.7 - Make a rough estimate of how far food coloring (or...Ch. 1.7 - Prob. 68PCh. 1.7 - Imagine a narrow pipe, filled with fluid, in which...Ch. 1.7 - Prob. 70P
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- Consider the Maxwell-Boltzmann distribution function plotted in Problem 28. For those parameters, determine the rms velocity and the most probable speed, as well as the values of f(v) for each of these values. Compare these values with the graph in Problem 28. 28. Plot the Maxwell-Boltzmann distribution function for a gas composed of nitrogen molecules (N2) at a temperature of 295 K. Identify the points on the curve that have a value of half the maximum value. Estimate these speeds, which represent the range of speeds most of the molecules are likely to have. The mass of a nitrogen molecule is 4.68 1026 kg. Equation 20.18 can be used to find the rms velocity given the temperature, Boltzmanns constant, and the mass of the atom or molecule. The mass of a nitrogen molecule is 4.68 1026 kg. vrms=3kBTm=3(1.381023J/K)4.681026kg=511m/s Using the results of Problem 28 and the rms velocity, we can calculate the value of f(v). f(vrms) = (3.11 108)(511)2 e(5.75106(511)2) = 0.00181 The most probable speed, for which this function has its maximum value, is given by Equation 20.20. vmp=2kBTm=2(1.381023J/K)(295K)4.681026kg=417m/s f(vmp) = (3.11108)(417)2 e(5.75106(417)2) = 0.00199 We plot these points on the speed distribution. The most probable speed is indeed at the peak of the distribution function. Since the function is not symmetric, the rms velocity is somewhat higher than the most probable speed. Figure P20.29ANSarrow_forwardFrom the MaxwellBoltzmann speed distribution, show that the most probable speed of a gas molecule is given by Equation 16.23. Note: The most probable speed corresponds to the point at which the slope of the speed distribution curve dNv/dv is zero.arrow_forwardTwo monatomic ideal gases A and B are at the same temperature. If 1.0 g of gas A has the same internal energy as 0.10 g of gas B, what are (a) the ratio of the number of moles of each gas and (b) the ration of the atomic masses of the two gases?arrow_forward
- Eight bumper cars, each with a mass of 322 kg. are running in a room 21.0 m long and 130 m wide. They have no driver, so they just bounce around on their own. The rms speed of the cars is 2.50 m/s. Repeating the arguments of Pressure, Temperature, and RMS Speed, find the average force per unit length (analogous to Pressure) that the cars exert the walls.arrow_forwardUsing the approximation v1v1+v f(v)dvf(v1)v for small v , estimate the fraction of nitrogen molecules at a temperature of 3.00102 K that have speeds between 290 m/s and 291 m/s.arrow_forwardCylinder A contains oxygen (O2) gas, and cylinder B contains nitrogen (N2) gas. If the molecules in the two cylinders have the same rms speeds, which of the following statements is false? (a) The two gases haw different temperatures. (b) The temperature of cylinder B is less than the temperature of cylinder A. (c) The temperature of cylinder B is greater than the temperature of cylinder A. (d) The average kinetic energy of the nitrogen molecules is less than the average kinetic energy of the oxygen molecules.arrow_forward
- An aluminum rod 0.500 m in length and with a cross-sectional area of 2.50 cm2 is inserted into a thermally insulated vessel containing liquid helium at 4.20 K. The rod is initially at 300 K. (a) If one-half of the rod is inserted into the helium, how many liters of helium boil off by the time the inserted half cools to 4.20 K? Assume the upper half does not yet cool. (b) If the circular surface of the upper end of the rod is maintained at 300 K, what is the approximate boil-off rate of liquid helium in liters per second after the lower half has reached 4.20 K? (Aluminum has thermal conductivity of 3 100 W/m K at 4.20 K; ignore its temperature variation. The density of liquid helium is 125 kg/m3.)arrow_forwardOne cylinder contains helium gas and another contains krypton gas at the same temperature. Mark each of these statements true, false, or impossible to determine from the given information. (a) The rms speeds of atoms in the two gases are the same. (b) The average kinetic energies of atoms in the two gases are the same. (c) The internal energies of 1 mole of gas in each cylinder are the same. (d) The pressures in the two cylinders ale the same.arrow_forwardFor a temperature increase of 10 at constant volume, what is the heat absorbed by (a) 3.0 mol of a dilute monatomic gas; (b) 0.50 mol of a dilute diatomic gas; and (c) 15 mol of a dilute polyatomic gas?arrow_forward
- Can carbon dioxide be liquefied at room temperature (20 If so, how? If not, why not? (See the phase diagram in the preceding problem.)arrow_forwardWhat is the average velocity of the air molecules in the room where you are right now?arrow_forwardA sample of a monatomic ideal gas occupies 5.00 L at atmospheric pressure and 300 K (point A in Fig. P17.68). It is warmed at constant volume to 3.00 atm (point B). Then it is allowed to expand isothermally to 1.00 atm (point C) and at last compressed isobarically to its original state. (a) Find the number of moles in the sample. Find (b) the temperature at point B, (c) the temperature at point C, and (d) the volume at point C. (e) Now consider the processes A B, B C, and C A. Describe how to carry out each process experimentally. (f) Find Q, W, and Eint for each of the processes. (g) For the whole cycle A B C A, find Q, W, and Eint. Figure P17.68arrow_forward
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