Essential University Physics
4th Edition
ISBN: 9780134988559
Author: Wolfson, Richard
Publisher: Pearson Education,
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 18, Problem 52P
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 solution
Students 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.
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.
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.
Chapter 18 Solutions
Essential University Physics
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 - Why cant an irreversible process be described by a...Ch. 18 - Are the initial and final equilibrium states of an...Ch. 18 - Prob. 5FTDCh. 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 - Three identical gas-cylinder systems are...Ch. 18 - Prob. 10FTDCh. 18 - Prob. 11ECh. 18 - Prob. 12ECh. 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. 22ECh. 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. 27ECh. 18 - Prob. 28ECh. 18 - Example 18.2: A gas bubble develops from...Ch. 18 - Prob. 30ECh. 18 - Example 18.2: A spherical balloon is placed inside...Ch. 18 - Prob. 32ECh. 18 - Example 18.4: An ideal gas with γ = 40 and...Ch. 18 - Prob. 34ECh. 18 - Example 18.4: An ideal gas with γ = 1.40 is...Ch. 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. 44PCh. 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. 49PCh. 18 - By what factor does the internal energy of an...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 - Prob. 56PCh. 18 - Youre the product safety officer for a company...Ch. 18 - Figure 18.22 shows data and a fit curve from an...Ch. 18 - Gasoline and diesel engines often use...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 - Prob. 70PCh. 18 - Prob. 71PCh. 18 - The table below shows measured values of pressure...Ch. 18 - Air with initial volume V0 = 4.50 L and initial...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 - A power plant extracts thermal energy from its...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
(a) What is the period of rotation of Earth in seconds? (b) What is the angular velocity of Earth? (c) Given th...
College Physics
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)
22. At what speed as a fraction of c, will a moving rod have a length 60% that of an identical rod at rest?
College Physics: A Strategic Approach (3rd Edition)
The Rankine temperature scale (abbreviatedR) uses the same size degrees as Fahrenheit, but measured up from abs...
An Introduction to Thermal Physics
49. A gray kangaroo can bound across level ground with each jump carrying it 10 m from the takeoff point. Typic...
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
The force, when you push against a wall with your fingers, they bend.
Conceptual Physics (12th Edition)
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_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_forwardA diatomic ideal gas at pressure p and volume V is expanding to three times its initial volume under constant pressure. In terms of p and V, calculate the change in internal energy ΔU.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_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
- The 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_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