Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 18, Problem 50P
Prove that the slope of an adiabat at a given point in a pV diagram is γ times the slope of the isotherm passing through the same point.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Consider the earth's atmosphere as an ideal gas of molecular weignt u in a
uniform gravitational field. Let g denotc the acceleration due to gravity.
(a) If z denotes the height above sea level, show that the change of atmos-
pheric pressure p with height is given by
dp
where T is the absolute temperature at the height z.
(6) If the decrease of pressure in (a) is due to an adiabatic expansion, show
that
dp
Y dT
Y -iT
(c) From (a) and (b) calculate dT/dz in degrees per kilometer. Assume
the atmosphere to consist mostly of nitrogen (N) gas for which y - 1.4.
(d) In an isothermal atmosphere at temperature T, express the pressure
p at height z in terms of the pressure po at sea level.
(e) If the sea-level pressure and temperature are po and To, respectively, and
the atmosphere is regarded as adiabatic as in part (b), find again the pressure
p at height z.
On the PV diagram for an ideal gas, one isothermal curve and one adiabatic curve pass through each point as shown. Prove that the slope of the adiabatic curve is steeper than the slope of the isotherm at that point by the factor γ.
Show that the isothermal compressibility KT and the adiabatic compressibility KS of a Bose ideal gas are given by in the picture.
where n(=N/V) is the density of the particles in the gas.
Chapter 18 Solutions
Essential University Physics (3rd Edition)
Ch. 18.2 - Two identical gas-cylinder systems are taken from...Ch. 18.2 - Name the basic thermodynamic process involved when...Ch. 18.3 - The same amount of heat flows into equal volumes...Ch. 18 - Prob. 1FTDCh. 18 - Prob. 2FTDCh. 18 - Prob. 3FTDCh. 18 - Why cant an irreversible process be described by a...Ch. 18 - Are the initial and final equilibrium states of an...Ch. 18 - Does the first law of thermodynamics apply to...Ch. 18 - Prob. 7FTD
Ch. 18 - Figure 18.18 shows two processes, A and B. that...Ch. 18 - When you let air out of a tire, the air seems...Ch. 18 - Blow on the back of your hand with your mouth wide...Ch. 18 - You boil water in an open pan. Of which of the...Ch. 18 - Three identical gas-cylinder systems are...Ch. 18 - Prob. 13FTDCh. 18 - In what sense can a gas of diatomic molecules be...Ch. 18 - Prob. 15ECh. 18 - Prob. 16ECh. 18 - A 40-W heat source is applied to a gas sample for...Ch. 18 - Find the rate of heat flow into a system whose...Ch. 18 - In a certain automobile engine, 17% of the total...Ch. 18 - An ideal gas expands from the state (p1, V1) to...Ch. 18 - Repeat Exercise 20 for a process that follows the...Ch. 18 - A balloon contains 0.30 mol of helium. It rises,...Ch. 18 - The balloon of Exercise 22 starts at 100 kPa...Ch. 18 - How much work does it take to compress 2.5 mol of...Ch. 18 - By what factor must the volume of a gas with =...Ch. 18 - Prob. 26ECh. 18 - A carbon-sequestration scheme calls for...Ch. 18 - A gas mixture contains 2.5 mol of O2 and 3.0 mol...Ch. 18 - A mixture of monatomic and diatomic gases has...Ch. 18 - What should be the approximate specific-heat ratio...Ch. 18 - Prob. 31ECh. 18 - An ideal gas expands to 10 times its original...Ch. 18 - During cycling, the human body typically releases...Ch. 18 - A 0.25-mol sample of ideal gas initially occupies...Ch. 18 - As the heart beats, blood pressure in an artery...Ch. 18 - It takes 1.5 kJ to compress a gas isothermally to...Ch. 18 - A gas undergoes an adiabatic compression during...Ch. 18 - A gas with = 1.40 occupies 6.25 L when its at...Ch. 18 - A gas sample undergoes the cyclic process ABCA...Ch. 18 - Prob. 40PCh. 18 - A gasoline engine has compression ratio 8.5 (sec...Ch. 18 - By what factor must the volume of a gas with =...Ch. 18 - Volvos B5340 engine, used in the V70 series cars,...Ch. 18 - A research balloon is prepared for launch by...Ch. 18 - Prob. 45PCh. 18 - By what factor does the internal energy of an...Ch. 18 - An ideal monatomic gas is compressed to half its...Ch. 18 - A gas expands isothermally from state A to state...Ch. 18 - A 3.50-mol sample of ideal gas with molar specific...Ch. 18 - Prove that the slope of an adiabat at a given...Ch. 18 - An ideal gas with = 1.67 starts at point A in...Ch. 18 - The gas of Example 18.4 starts at state A in Fig....Ch. 18 - The gas of Example 18.4 starts at state A in Fig....Ch. 18 - A 25-L sample of ideal gas with = 1.67 is at 250...Ch. 18 - Prob. 55PCh. 18 - A 25-L sample of ideal gas with = 1.67 is at 250...Ch. 18 - Youre the product safety officer for a company...Ch. 18 - Figure 18.22 shows data and a fit curve from an...Ch. 18 - External forces compress 21 mol of ideal monatomic...Ch. 18 - A gas with = 7/5 is at 273 K when its compressed...Ch. 18 - An ideal gas with = 1.3 is initially at 273 K and...Ch. 18 - The curved path in Fig. 18.23 lies on the 350-K...Ch. 18 - Repeat part (a) of Problem 62 for the path ACDA in...Ch. 18 - A gas mixture contains monatomic argon and...Ch. 18 - How much of a triatomic gas with Cv = 3R would you...Ch. 18 - An 8.5-kg rock at 0C is dropped into a...Ch. 18 - A piston-cylinder arrangement containing 0.30 mol...Ch. 18 - Experimental studies show that the pV curve for a...Ch. 18 - Show that the application of Equation 18.3 to an...Ch. 18 - A horizontal piston-cylinder system containing n...Ch. 18 - Prob. 71PCh. 18 - The table below shows measured values of pressure...Ch. 18 - In a reversible process, a volume of air V0= 17 m3...Ch. 18 - A real gas is more accurately described using the...Ch. 18 - Repeat Exercise 20 for an expansion along the path...Ch. 18 - The adiabatic lapse rate is the rate at which air...Ch. 18 - The nuclear power plant at which youre the public...Ch. 18 - Prob. 78PCh. 18 - One scheme for reducing greenhouse-gas emissions...Ch. 18 - Warm winds called Chinooks (a Native-American term...Ch. 18 - Warm winds called Chinooks (a Native-American term...Ch. 18 - Warm winds called Chinooks (a Native-American term...Ch. 18 - Warm winds called Chinooks (a Native-American term...
Additional Science Textbook Solutions
Find more solutions based on key concepts
What class of motion, natural or violent, did Aristotle attribute to motion of the Moon?
Conceptual Physics (12th Edition)
Express the units of angular momentum (a) using only the fundamental units kilogram, meter, and second; (b) in ...
Essential University Physics: Volume 1 (3rd Edition)
3. What is free-fall, and why does it make you weightless? Briefly describe why astronauts are weightless in th...
The Cosmic Perspective (8th Edition)
7.14 •• An ideal spring of negligible mass is 12.00 cm long when nothing is attached to it. When you hang a 3.1...
University Physics with Modern Physics (14th Edition)
The pV-diagram of the Carnot cycle.
Sears And Zemansky's University Physics With Modern Physics
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
- Calculate the values of q, w, delta U, and delta H for the reversible adiabatic expansion of 1 mole of a monatomic ideal gas from 5.00m^3 to 25 m^3. The temperature of the gas is initially 298K.arrow_forwardShow that the following relations hold for a reversible adiabatic expansion of an ideal gas: TV-1 = a constant T = another constant pl-1/y The fireball of a uranium fission bomb consists of a sphere of gas of radius 15 m and temperature 300,000 K shortly after detonation. Assuming that the expansion is adiabatic and that the fireball remains spherical, estimate the radius of the ball when the temperature is 3000 K. (Take y = 1.4 for air.)arrow_forwardFind q, △U, and the work done along the isotherm AB for a mono atomic ideal gas. The temperature of the isotherm is 20.0 Celsius.arrow_forward
- Determine the heat capacity at constant pressure (in Joule per kelvin per mole) for an ideal monoatomic. NOTE: Express answer in THREE SIGNIFICANT FIGURES.arrow_forwardProve that the CV of an ideal gas only functions Tarrow_forwardThe volume of 2 moles of a diatomic ideal gas at 300 K is doubled keeping its pressure constant. Find the change in the internal energy of the gas. Given R = 8.3 JK- mol.arrow_forward
- The volume of a monatomic ideal gas doubles in an adiabatic expansion. By what factor do (a) the pressurearrow_forwardThe only form of energy possessed by molecules of a monatomic ideal gas is translational kinetic energy. From kinetic, the average kinetic energy per molecule is KEmolecule = 3 2 kBT = 3 2 R NA T Use these results to show that the internal energy of a monatomic ideal gas at pressure P and occupying volume V may be written as U = 3 2 PV.arrow_forwardGive 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_forward
- One mole of a monatomic ideal gas is initially at 273 K and 1 atm. (a) What is its initial internal energy? (b) Find its final internal energy and the work done by the gas when 500 J of heat are added at constant pressure. (c) Find the same quantities when 500 J of heat are added at constant volume.arrow_forwardA sample consists of an amount n in moles of a monatomic ideal gas. The gas expands adiabatically, with work W done on it. (Work W is a negative number.) The initial temperature and pressure of the gas are Ti and Pi. Calculate (a) the final temperature and (b) the final pressure.arrow_forwardOne mole of ideal gas at 2 atm and 300 K is expanded isothermally to 1 atm while in contact with a heat sink at 400 K. Find del S for the gas and the heat sink if the expansion is reversiblearrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Thermodynamics: Crash Course Physics #23; Author: Crash Course;https://www.youtube.com/watch?v=4i1MUWJoI0U;License: Standard YouTube License, CC-BY