An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 1.7, Problem 65P
To determine
A rough estimate of
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Pretend that you live in the 19th century and don't know the value of Avogadro's number* (or of Boltzmann's constant or of the mass or size of any molecule). Show how you could make a rough estimate of Avogadro's number from a measurement of the thermal conductivity of a gas, together with other measurements that are relatively easy.
In this problem you are to consider an adiabaticexpansion of an ideal diatomic gas, which means that the gas expands with no addition or subtraction of heat.
Assume that the gas is initially at pressure p0, volume V0, and temperature T0. In addition, assume that the temperature of the gas is such that you can neglect vibrational degrees of freedom. Thus, the ratio of heat capacities is γ=Cp/CV=7/5.
Note that, unless explicitly stated, the variable γshould not appear in your answers--if needed use the fact that γ=7/5 for an ideal diatomic gas.
Find an analytic expression for p(V), the pressure as a function of volume, during the adiabatic expansion.
Express the pressure in terms of V and any or all of the given initial values p0, T0, and V0.
p(V) = __________
In this problem you are to consider an adiabaticexpansion of an ideal diatomic gas, which means that the gas expands with no addition or subtraction of heat.
Assume that the gas is initially at pressure p0, volume V0, and temperature T0. In addition, assume that the temperature of the gas is such that you can neglect vibrational degrees of freedom. Thus, the ratio of heat capacities is γ=Cp/CV=7/5.
Note that, unless explicitly stated, the variable γshould not appear in your answers--if needed use the fact that γ=7/5 for an ideal diatomic gas.
A) Find an analytic expression for p(V), the pressure as a function of volume, during the adiabatic expansion.
Express the pressure in terms of V and any or all of the given initial values p0, T0, and V0.
p(V) = __________
B) At the end of the adiabatic expansion, the gas fills a new volume V1, where V1>V0. Find W, the work done by the gas on the container during the expansion.
Express the work in terms of p0, V0, and V1. Your…
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
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Give the temperature T of 1 mole of ideal gas as a function of the pressure P, volume V, and the gas constant R and give the internal energy U of a rigid diatomic ideal gas as a function of its temperature T and the gas constant R.arrow_forwardA diatomic ideal gas at pressure p and volume V is expanding to three times its initial volume under constant pressure. W=2pV. a) If the initial temperature equals T, express the final temperature Tf in terms of the original temperature T. b) In terms of p and V, calculate the expression of the heat Q flowing into the gas. c) In terms of p and V, calculate the expression of the change in internal energy ΔU.arrow_forwardCan you show that ∂U/∂P )T =0 J/Pa for a perfect gas? Hint: Start with ∂U = T ∂S − P ∂V. Quickly, you will come to a derivative of entropy; to get rid of it to answer the question, use a Maxwell relation.arrow_forward
- The molar heat capacity at constant volume of a monoatomic ideal gas is (3/2)R,but the molar heat capacity at constant volume of a diatomic ideal gas is (5/2)R. Whyare the values differentarrow_forwardAn ideal diatomic gas, with molecular rotation but without any molecular oscillation, loses a certain amount of energy as heat Q. Is the resulting decrease in the internal energy of the gas greater if the loss occurs in a constant-volume process or in a constant-pressure process?arrow_forwardA diatomic ideal gas at pressure p and volume V is expanding to three times its initial volume under constant pressure. If the initial temperature equals T, express the final temperature Tf in terms of the original temperature T. In terms of p and V, calculate the work W done by the gas. In terms of p and V, calculate the heat Q flowing into the gas.arrow_forward
- Compare the charge in the internal energy of an ideal gas for a quasi-static adiabatic expansion with that for a quasi-static isothermal expansion. What happens to the temperature of an ideal gas in an adiabatic expansion?arrow_forwardThe constant volume heat capacity of an ideal monatomic gas is 3R/2, but the constantvolume heat capacity of an ideal diatomic gas is 5/2. Why are the values different?arrow_forwardHow would the temperature of a REAL gas (not perfect) in a reversible adiabatic expansion be affected?arrow_forward
- Calculate the Helmholtz free energy (∆A) of an ideal gas when 2.0 mol expands isothermally from 1.5 to 3.5 cm3 at 120°Carrow_forwardConsider one mole of a simple ideal gas enclosed in a cylindrical piston with rigid impermeable adiabatic walls. The piston has a cross sectional area ofA = 0.10 m^2 and the cylinder enclosing the gas has a height of h = 1.0 cm. The gas inside the piston has a temperature T = 300.K. Recall that the internal energy for an ideal gas is U= n cV,mT, where cV,m= 1.5 R is the molar heat capacity for the ideal gas. Calculate the pressure and the internal energy of the ideal gas.arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning