PHY 4513 / PHY 5515 : Thermal and Statistical
Physics - Spring 2025
Homework Set # 1
Due date: Please check corresponding Canvas assignment
1. (2 pts) We discussed how the zeroth law of thermodynamics basically ensures that
thermometers work. Now, building useful phenomenological thermometers requires
a series of characteristics. One of them is that the material used for the thermometer
should have a specific heat much smaller than that of the object to which the
temperature is measured. We can state this as ϵ=CT/CM≪1, where CTis the
heat capacity of the thermometer, and CMthat one of the object. Show that with
this assumption, when the initial temperature of the thermometer is T1and the
initial temperature of the object is T2, they are put in thermal contact and after
some time thermalized to a final temperature Tf, then:
Tf≈T2+ (T1−T2)ϵ . (1)
Why is this an important condition for a good thermometer?
2. (2 pts) Answer the following questions:
(a) Does a thermometer measure its own temperature or the temperature of the
surroundings? Explain.
(b) Review the definition of Kelvin, Celsius, and Fahrenheit scales. What is the
relative sizes of the degree Kelvin, Celsius, and Fahrenheit.
(c) Global warming of earth’s surface is generally producing greater temperature
rises over land than over the oceans. Why might this be?
3. (2 pts) Problem (3.3) of your textbook (Blundell & Blundell)
4. (2 pts) Consider Example 4.4 of your textbook (see also the lecture notes
Intro part 2 PHY4513.pdf posted on Canvas). Compute the normalizing factor
needed to get the probability P(z) in equation (4.20) of your textbook (Hint: basi-
cally workout the normalized distribution that lets you replace the ∝sign by an =
sign in such equation.).
5. (2 pts) Problem (4.8) of your textbook.
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