An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter 1.6, Problem 44P
To determine
To Check:Most of the values of
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Problem 1:
In statistical mechanics, the internal energy of an ideal gas is given by:
N.
aNkB
2/3
(3NKB
U = U(S,V) =
е
where a is a constant.
1- Show that the variation of the internal energy is given by:
2
dS -
\3V
2
dU =
dV
\3NkB
2- Using the fundamental relation of thermodynamic dU = T.ds – p. dV, show that the equation of
state PV = nRT follows from the first expression of U.
Using the graph below and by considering the fundamental
equation of thermodynamics, justify the differences in
behaviours of Gibbs as a function of pressure for gaseous, liquid
and solid forms of a substance.
Gas
Liquid
Solid
Pressure, p
The molar volume of liquid water is 18.05 cm³. By considering
the fundamental equation of chemical thermodynamics,
calculate the change in molar Gibbs energy, dG,
when the pressure is increased by 0.1 bar.
Gibbs energy, G
a) Find the difference of molar-specific heats Cp - C, for the gas
covered by the equation of state:
(P+) (V - b) = RT
b) Determine the volume of the hypersphere in N-dimensional
space.
c) An ideal gas consists of N monatomic molecules. Using the grand
canonical ensemble, (T-μ) distribution, calculate the chemical
potential, pressure, and entropy.
Chapter 1 Solutions
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
Knowledge Booster
Similar questions
- You are studying a gas known as "gopherine" and looking in the literature you find that someone has reported the partition function for one molecule of this gas, 5/2 AzT q(V, T) = ) %3D h?m Assume that the molecules are independent and indistinguishable. Derive the expressions for the energy, (E), for this gas. Give your answers in terms of N, kg, T. V and the constants A and B. O (E) = NkaT ㅇ (E) =D NkaT ㅇ (E) %3D NkaT- O (E) = ANKET - O (E) = - T ㅇ (E)=D 쑤-arrow_forward1.50 moles of a monatomic ideal gas goes isothermally from state 1 to state 2. P1 = 2.8×105 Pa, V1 = 88 m3, and P2 = 6.6×105 Pa. What is the volume in state 2, in m3? Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.arrow_forwardWrite the mathematical relationships for each of the following Conclude the thermodynamic properties (parameters) of ideal gas same as ( energy , prussure, entropy , specific heat at fixed prussure , specific heat at fixed volume ) e 12:31 Varrow_forward
- dU =T dS – P dV Re-arrange the thermodynamic identity by solving for dS. Assume we are applying this new expression to an ideal gas, re-write the du term in terms of the appropriate heat capacity and temperature. Re-write the coefficient of the dV term in terms of volume. Connect these “classical" expressions for entropy to the "modern" interpretation where we are concerned with the uncertainty associated with position and momentum of the particles in an ideal gas. Answer with sentences. Now, re-write the expression in terms of enthalpy so you can connect entropy with enthalpy. Expalin why this final expression makes sense.arrow_forwardA bottle of volume V = 0.15 m³ contains helium gas (a monatomic gas) at a pressure p = 722,266 Pa (Pascal = N/m² and temperature T = 300 K. Calculate a numerical value for the internal energy U of this gas. Include units in your answer, using Sl units (m for meters, kg for kilograms, s for seconds, J for joules, K for kelvin, etc.). Write your answer as an exponential as described in the instructions.arrow_forwardConsider a Carnot engine operating between 75 degrees Celsius and 25 degrees Celsius using one mole of an ideal, diatomic gas. If V1 = 0.01 cubic meter and V2 = 0.10 cubic meter, answer the questions that follow. (C). What is qh (in Joules)? Express answer in THREE SIGNIFICANT FIGURES? (D). What is qc (in Joules)? Express answer in THREE SIGNIFICANT FIGURES? (E). What is the total work (in Joules)? Express answer in THREE SIGNIFICANT FIGURES?arrow_forward
- Derive the thermodynamic equation of state from the fundamental equation for enthalpy (OT), ән (OH!) T =V-T HINT: you will need to use a Maxwell relation. Derive an expression for an ideal and (b) a van der Waals gas. ән Әр T for (a)arrow_forwardRather than insisting that all the molecules be in the left half of a container, suppose we only require that they be in the leftmost 99% (leaving the remaining 1% completely empty). What is the probability of finding such an arrangement if there are 100 molecules in the container? What if there are 10,000 molecules? What if there are 1023 ?arrow_forwardConsider an ideal gas of N molecules, in equilibrium in a container of volume V . Calculatea. the probability p1 of finding all molecules concentrated in a volume V /3 (macrostate 1);b. the probability p2 of finding all molecules concentrated in a volume 2V /3 (macrostate 2);c. the probability p of finding N/3 of the molecules concentrated in a volume V / 3 and the othersin the remaining volume;d. the entropy difference ∆S = S2 - S1 between states 1 and 2;e. the numerical values of p1, p2, and p for N = 9.arrow_forward
- Calculate the number of microstates that are available in a single atom of carbon in graphite.The standard molar entropy (S°) of carbon is 5.7 J/(mol · K) and the Boltzmann constant (kB) is1.381 × 10 ―23?/?. HELP PLEASEarrow_forwardAn approximate partition function for a gas of hard spheres can be obtained from the partition function of a monatomic gas by by V-b, where b is related to the volume of the W hard spheres. Derive expressions for the energy and the pressure of this system. (Use the following as necessary: b, kg, N, T, and V.) replacing V in Q(N, V, B) = [9(V, P)] (where q(V, B) = (22m) 3/2v) by V N! h²ß (E) (P) =arrow_forwardA sample of a monatomic ideal gas occupies 5.00 L at atmospheric pressure and 300 K (point A in the figure below). 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. Р (atm) 3 B 1 V (L) 5 10 15 (a) Find the number of moles in the sample. moles (b) Find the temperature at point B. K (c) Find the temperature at point C. (d) Find the volume at point C. L (e) Now consider the processes A - B, B → C, and C- A. Describe how to carry out each process experimentally.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning