Concept explainers
Because osmotic pressures can be quite large, you may wonder whether the approximation made in equation 5.74 is valid in practice: Is
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
An Introduction to Thermal Physics
Additional Science Textbook Solutions
Physics for Scientists and Engineers with Modern Physics
Modern Physics
Conceptual Physical Science (6th Edition)
Glencoe Physical Science 2012 Student Edition (Glencoe Science) (McGraw-Hill Education)
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
College Physics: A Strategic Approach (4th Edition)
- The Clausius-Clapeyron relation 5.47 is a differential equation that can, in principle, be solved to find the shape of the entire phase-boundary curve. To solve it, however, you have to know how both L and ~V depend on temperature and pressure. Often, over a reasonably small section of the curve, you can take L to be constant. Moreover, if one of the phases is a gas, you can usually neglect the volume of the condensed phase and just take ~V to be the volume of the gas, expressed in terms of temperature and pressure using the ideal gas law. Making all these assumptions, solve the differential equation explicitly to obtain the following formula for the phase boundary curve:This result is called the vapor pressure equation. Caution: Be sure to use this formula only when all the assumptions just listed are valid.arrow_forwardUsing MATLAB editor, make a script m-file which includes a header block and comments: Utilizing the ideal gas law: Vmol= RT/P Calculate the molecular volume where: R = 0.08206 L-atm/(mol-K) P = 1.015 atm. and T = 270 - 315 K in 5 degree increments Make a display matrix which has the values of T in the first column and Vmol in the second column Save the script and publish function to create a pdf file from the script in a file named "ECE105_Wk2_L1_Prep_1"arrow_forwardInterstellar space is quite different from the gaseous environments we commonly encounter on Earth. For instance, a typical density of the medium is about 1 atom cm−3 and that atom is typically H; the effective temperature due to stellar background radiation is about 10 kK. Estimate the diffusion coefficient and thermal conductivity of H under these conditions. Compare your answers with the values for gases under typical terrestrial conditions. Comment: Energy is in fact transferred much more effectively by radiation.arrow_forward
- The only form of energy possessed by molecules of a monatomic ideal gas is translational kinetic energy. Using the results from the discussion of kinetic theory in Section 10.5, show that the internal energy of a monatomic ideal gas at pressure P and occupying volume V may be written as U = 3/2PVarrow_forwardProvide an equation of state (relating pressure, volume and temperature) for a real gas and interpret the terms that take into account the differences between a real and ideal gas. Comment on the extreme limits (example:zero temperature). Under what conditions does the behavior of real gases conform to the behavior expected to ideal gases?arrow_forwardPlease answer all parts: Problem 3: There are lots of examples of ideal gases in the universe, and they exist in many different conditions. In this problem we will examine what the temperature of these various phenomena are. Part (a) Give an expression for the temperature of an ideal gas in terms of pressure P, particle density per unit volume ρ, and fundamental constants. T = ______ Part (b) Near the surface of Venus, its atmosphere has a pressure fv= 91 times the pressure of Earth's atmosphere, and a particle density of around ρv = 0.91 × 1027 m-3. What is the temperature of Venus' atmosphere (in C) near the surface? Part (c) The Orion nebula is one of the brightest diffuse nebulae in the sky (look for it in the winter, just below the three bright stars in Orion's belt). It is a very complicated mess of gas, dust, young star systems, and brown dwarfs, but let's estimate its temperature if we assume it is a uniform ideal gas. Assume it is a sphere of radius r = 5.7 × 1015 m…arrow_forward
- Hi, could I get some help with this macro-connection physics problem involving moles and the Ideal Gas Law? The set up is: How many moles are there in a cubic meter of an ideal gas at 100 degree celsius (C) to 4 digits of precision with a pressure of 0.25 atm, assuming 1 atm = 101325 N/m2 with kB = 1.38e-23 J/K and NA = 6.022e23? Thank you.arrow_forwardThe following data (figure) describe the diffusion of a substitutional impurity atom in a polycrystalline solid. Each data set below (A, B, and C) is associated with a characteristic diffusion environment for the impurity atom. The possible diffusion environments are: surface diffusion, volume diffusion, grain boundary diffusion. Based on your understanding of solid-state diffusion mechanisms and processes, name the diffusion environment most likely associated with each data set:arrow_forwardConsider an ideal gas at temperature T = 578 K and pressure p = 2 atm. Calculate the average volume per molecule in this gas in units of cubic nanometers (a nanometer is 10-9 m). Do not include units in your answer and state your answer as a number in normal form.arrow_forward
- Consider phase transitions in conditions of variable pressure, volume and temperature. In the phase diagram for a single component system, the critical point defines the pressure, Pc, and temperature, Tc, at the end of the liquid-vapour co-existence line in P-T coordinates. A system consists of one mole of van der Waals gas, whose equation of state is P+ (V - b) = RT , where R is the universal gas constant. Using the information from (a) (ii), show that, for such a system, the molar volume at the critical point is given by V. = 3b. Show also that the other two parameters at the critical point are 8a and Pc Tc 27 Rb a 27b2arrow_forwardIn the simple kinetic theory of a gas we discussed in class, the molecules are assumed to be point-like objects (without any volume) so that they rarely collide with one another. In reality, each molecule has a small volume and so there are collisions. Let's assume that a molecule is a hard sphere of radius r. Then the molecules will occasionally collide with each other. The average distance traveled between two successive collisions (called mean free path) is λ = V/(4π √2 r2N) where V is the volume of the gas containing N molecules. Calculate the mean free path of a H2 molecule in a hydrogen gas tank at STP. Assume the molecular radius to be 10-10 a) 2.1*10-7 m b) 4.2*10-7 m c) none of these.arrow_forwardI just need help with part D Problem 6: There are lots of examples of ideal gases in the universe, and they exist in many different conditions. In this problem we will examine what the temperature of these various phenomena are. Part (a) Give an expression for the temperature of an ideal gas in terms of pressure P, particle density per unit volume ρ, and fundamental constants. Answer: T = P/( ρ kB ) Part (b) Near the surface of Venus, its atmosphere has a pressure fv= 96 times the pressure of Earth's atmosphere, and a particle density of around ρv = 0.92 × 1027 m-3. What is the temperature of Venus' atmosphere (in C) near the surface? Answer: Tv = 490.55 Part (c) The Orion nebula is one of the brightest diffuse nebulae in the sky (look for it in the winter, just below the three bright stars in Orion's belt). It is a very complicated mess of gas, dust, young star systems, and brown dwarfs, but let's estimate its temperature if we assume it is a uniform ideal gas. Assume it is a…arrow_forward
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON