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Chapter 1: Q.1.23 (page 17)
Calculate the total thermal energy in a liter of helium at room temperature and atmospheric pressure. Then repeat the calculation for a liter of air.
The total thermal energy in a liter is for helium and for air.
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Problem 1.41. To measure the heat capacity of an object, all you usually have to do is put it in thermal contact with another object whose heat capacity you know. As an example, suppose that a chunk of metal is immersed in boiling water (100掳C), then is quickly transferred into a Styrofoam cup containing 250 g of water at 20掳C. After a minute or so, the temperature of the contents of the cup is 24掳C. Assume that during this time no significant energy is transferred between the contents of the cup and the surroundings. The heat capacity of the cup itself is negligible.
Problem 1.49. Consider the combustion of one mole of with mole of under standard conditions, as discussed in the text. How much of the heat energy produced comes from a decrease in the internal energy of the system, and how much comes from work done by the collapsing atmosphere? (Treat the volume of the liquid water as negligible.)
Does it ever make sense to say that one object is "twice as hot" as another? Does it matter whether one is referring to Celsius or Kelvin temperatures? Explain.
A mole is approximately the number of protons in a gram of protons. The mass of a neutron is about the same as the mass of a proton, while the mass of an electron is usually negligible in comparison, so if you know the total number of protons and neutrons in a molecule(i,e., its "atomic mass"), you know the approximate mass(in grams) of a mole of these molecules. Referring to the periodic table at the back of this book ,find the mass of a mole of each of the following : Water, nitrogen (N2), lead, quartz (Si O2)
Measured heat capacities of solids and liquids are almost always at constant pressure, not constant volume. To see why, estimate the pressure needed to keep fixed as increases, as follows.
(a) First imagine slightly increasing the temperature of a material at constant pressure. Write the change in volume,, in terms of and the thermal expansion coefficient introduced in Problem 1.7.
(b) Now imagine slightly compressing the material, holding its temperature fixed. Write the change in volume for this process, , in terms of and the isothermal compressibility , defined as
(c) Finally, imagine that you compress the material just enough in part (b) to offset the expansion in part (a). Then the ratio of is equal to , since there is no net change in volume. Express this partial derivative in terms of . Then express it more abstractly in terms of the partial derivatives used to define . For the second expression you should obtain
This result is actually a purely mathematical relation, true for any three quantities that are related in such a way that any two determine the third.
(d) Compute for an ideal gas, and check that the three expressions satisfy the identity you found in part (c).
(e) For water at . Suppose you increase the temperature of some water from . How much pressure must you apply to prevent it from expanding? Repeat the calculation for mercury, for which and
Given the choice, would you rather measure the heat capacities of these substances at constant or at constant ?
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