Chapter 5: 5.21 (page 166)
Is heat capacity (C) extensive or intensive? What about specific heat (c) ? Explain briefly.
Short Answer
Heat capacity is an extensive property
Specific heat is an intensive property.
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Chapter 5: 5.21 (page 166)
Is heat capacity (C) extensive or intensive? What about specific heat (c) ? Explain briefly.
Heat capacity is an extensive property
Specific heat is an intensive property.
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Assume that the air you exhale is at 35°C, with a relative humidity of 90%. This air immediately mixes with environmental air at 5°C and unknown relative humidity; during the mixing, a variety of intermediate temperatures and water vapour percentages temporarily occur. If you are able to "see your breath" due to the formation of cloud droplets during this mixing, what can you conclude about the relative humidity of your environment? (Refer to the vapour pressure graph drawn in Problem 5.42.)
Use a Maxwell relation from the previous problem and the third law of thermodynamics to prove that the thermal expansion coefficient (defined in Problem 1.7) must be zero at T=0.
Consider the production of ammonia from nitrogen and hydrogen,
N2 + 3H2 2NH3
at 298 K and 1 bar. From the values of and S tabulated at the back of this book, compute for this reaction and check that it is consistent with the value given in the table.
Problem 5.35. The Clausius-Clapeyron relation 5.47 is a differential equation that can, in principle, be solved to find the shape of the entire phase-boundary curve. To solve it, however, you have to know how both L and V depend on temperature and pressure. Often, over a reasonably small section of the curve, you can take L to be constant. Moreover, if one of the phases is a gas, you can usually neglect the volume of the condensed phase and just take V to be the volume of the gas, expressed in terms of temperature and pressure using the ideal gas law. Making all these assumptions, solve the differential equation explicitly to obtain the following formula for the phase boundary curve:
P= (constant) x e-L/RT
This result is called the vapour pressure equation. Caution: Be sure to use this formula only when all the assumptions just listed are valid.
The formula for Cp-Cv derived in the previous problem can also be derived starting with the definitions of these quantities in terms of U and H. Do so. Most of the derivation is very similar, but at one point you need to use the relation .
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