Chapter 3: Thermodynamics

a) A typical student listening attentively to a physics lecture has a heat output of $\mathbf{100}\mathbf{\hspace{0.33em}}\mathit{W}$. How much heat energy does a class of $\mathbf{140}$physics students release into a lecture hall over the course of a 50 min lecture? (b) Assume that all the heat energy in part (a) is transferred to the $\mathbf{3200}\mathbf{}{\mathbf{m}}^{\mathbf{2}}$of air in the room. The air has specific heat $\mathbf{1020}\mathbf{\hspace{0.33em}}\mathbf{J}\mathbf{/}\mathbf{kg}\mathbf{\cdot }\mathbf{K}$and density$\mathbf{1}\mathbf{.}\mathbf{20}\mathbf{}\mathbf{kg}\mathbf{/}{\mathbf{m}}^{\mathbf{3}}$. If none of the heat escapes and the air conditioning system is off, how much will the temperature of the air in the room rise during the $\mathbf{50}\mathbf{\hspace{0.33em}}\mathbf{min}$lecture? (c) If the class is taking an exam, the heat output per student rises to$\mathbf{280}\mathbf{}\mathbf{W}$ . What is the temperature rise during 50 min in this case?

The rate of effusion—that is, leakage of gas through tiny cracks—is proportional to vrms. If tiny cracks exist in the material that’s used to seal the space between two glass panes, how many times greater is the rate of He leakage out of the space between the panes than the rate of Xe leakage at the same temperature?

(a) 370 times; (b) 19 times;

(c) 6 times; (d) no greater—the He leakage rate is the same as for Xe.

The molar heat capacity of a certain substance varies with temperature according to the empirical equation

$\mathbf{C}\mathbf{=}\mathbf{}\mathbf{29}\mathbf{.}\mathbf{5}\mathbf{}\mathbf{J}\mathbf{/}\mathbf{mol}\mathbf{\times }\mathbf{K}\mathbf{}\mathbf{+}\mathbf{}\mathbf{(}\mathbf{8}\mathbf{.}\mathbf{20}\mathbf{}\mathbf{\times }\mathbf{}{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{}\mathbf{J}\mathbf{/}\mathbf{mol}\mathbf{\times }{\mathbf{K}}^{\mathbf{2}}\mathbf{)}\mathbf{T}$How much heat is necessary to change the temperature of 3.00 mol of this substance from $\mathbf{27}\mathbf{\hspace{0.33em}}\mathbf{º}\mathbf{C}$to $\mathbf{227}\mathbf{\hspace{0.33em}}\mathbf{º}\mathbf{C}$? (Hint: Use Eq. (17.18) in the form dQ = nCdT and integrate.)

Question: If the air temperature is the same as the temperature of your skin (about 30°C), your body cannot get rid of heat by transferring it to the air. In that case, it gets rid of the heat by evaporating water (sweat). During bicycling, a typical 70-kg person’s body produces energy at a rate of about 500W due to metabolism, 80% of which is converted to heat. (a) How many kilograms of water must the person’s body evaporate in an hour to get rid of this heat? The heat of vaporization of water at body temperature is $\mathbf{2}\mathbf{.}\mathbf{42}\mathbf{\times }{\mathbf{10}}^{\mathbf{6}}\mathbf{J}\mathbf{/}\mathbf{kg}$. (b) The evaporated water must, of course, be replenished, or the person will dehydrate. How many 750-mL bottles of water must the bicyclist drink per hour to replenish the lost water? (Recall that the mass of a litre of water is 1.0 kg.

A newspaper article about the weather states that “the temperature of a body measures how much heat the body contains.” Is this description correct? Why or why not?

You bake chocolate chip cookies and put them, still warm, in a container with a loose (not airtight) lid. What kind of process does the air inside the container undergo as the cookies gradually cool to room temperature (isothermal, isochoric, adiabatic, isobaric, or some combination)? Explain.

A rigid, perfectly insulated container has a membrane dividing its volume in half. One side contains a gas at an absolute temperature and pressure , while the other half is completely empty. Suddenly a small hole develops in the membrane, allowing the gas to leak out into the other half until it eventually occupies twice its original volume. In terms of and , what will be the new temperature and pressure of the gas when it is distributed equally in both halves of the container? Explain your reasoning.

An electric motor has its shaft coupled to that of an electric generator. The motor drives the generator, and some current from the generator is used to run the motor. The excess current is used to light a home. What is wrong with this scheme?

Shows a pV-diagram for an ideal gas in which its absolute temperature at b is one-fourth of its absolute temperature at a. (a) What volume does this gas occupy at point b? (b) How many joules of work was done by or on the gas in this process? Was it done by or on the gas? (c) Did the internal energy of the gas increase or decrease from a to b? How do you know? (d) Did heat enter or leave the gas from a to b? How do you know?

A welder using a tank of volume$\mathbf{0}\mathbf{.}\mathbf{0750}\mathbf{}{\mathbf{m}}^{\mathbf{3}}$fills it with oxygen (molar mass 32.0 g/mol) at a gauge pressure of$\mathbf{3}\mathbf{.}\mathbf{00}\mathbf{*}{\mathbf{10}}^{\mathbf{5}}\mathbf{Pa}$and temperature of$\mathbf{37}\mathbf{.}\mathbf{0}\mathbf{°}\mathbf{C}$. The tank has a small leak, and in time some of the oxygen leaks out. On a day when the temperature is$\mathbf{22}\mathbf{.}\mathbf{0}\mathbf{°}\mathit{C}$, the gauge pressure of the oxygen in the tank is$\mathbf{1}\mathbf{.}\mathbf{80}\mathbf{}\mathbf{*}\mathbf{}{\mathbf{10}}^{\mathbf{5}}\mathbf{Pa}$. Find (a) the initial mass of oxygen and (b) the mass of oxygen that has leaked out.