Concept explainers
(a)
The pressure at the center of sun.
Given:
Temperature at the center of the gas is 1 × 10 7 K .
Density at the center of sun is 1 × 10 5 kg / m 3 .
Formula used:
Write the expression for the ideal gas.
P V = n R T
Here, P is the pressure, V is the volume, n is the number of moles, R is the gas constant and T is the temperature.
Solve the above equation for P .
P = n R T V ........ (1)
Write the expression for the number of moles.
n p = m p M p ........ (2)
Here, n p is the number of moles of protons, m p is the mass of protons and M p is the molar ma of proton.
Calculation:
Substitute 10 5 kg for m p and 10 − 3 kg for M p in equation (2).
n p = 10 5 kg 10 − 3 kg n p = 10 8
The number of electrons is 2 × 10 8 .
Substitute 2 × 10 8 mol for n , 8.314 J / mol ⋅ K for R , 10 7 K for T and 1 m 3 for V in equation (1).
P = ( 2 × 10 8 ) ( 8.314 J / mol ⋅ K ) 10 7 K 1 m 3 P = 2 × 10 11 atm
Conclusion:
The pressure is 2 × 10 11 atm .
The pressure at the center of sun.
Given:
Temperature at the center of the gas is
Density at the center of sun is
Formula used:
Write the expression for the ideal gas.
Here,
Solve the above equation for
Write the expression for the number of moles.
Here,
Calculation:
Substitute
The number of electrons is
Substitute
Conclusion:
The pressure is
(a)
Explanation of Solution
Given:
Temperature at the center of the gas is
Density at the center of sun is
Formula used:
Write the expression for the ideal gas.
Here,
Solve the above equation for
Write the expression for the number of moles.
Here,
Calculation:
Substitute
The number of electrons is
Substitute
Conclusion:
The pressure is
(b)
The root mean square speed of electron and proton at the center of the sun.
(b)
Explanation of Solution
Given:
TheTemperature at the center of the gas is
Formula used:
Write the expression for the root mean square speed of the molecule.
Here,
Calculation:
Substitute
Substitute
Conclusion:
The rms speed of proton and electron at the center of sun is
Want to see more full solutions like this?
Chapter 17 Solutions
Physics for Scientists and Engineers
- You are on an interstellar mission from the Earth to the 8.7 light-years distant star Sirius. Your spaceship can travel with 70% the speed of light and has a cylindrical shape with a diameter of 6 m at the front surface and a length of 25 m. You have to cross the interstellar medium with anapproximated density of 1 hydrogen atom/m3.(a) Calculate the time it takes your spaceship to reach Sirius.(b) Determine the mass of interstellar gas that collides with your spaceship during the mission.Because you are moving at an enormous speed, your mission from the previous will be influenced by the effects of time dilation described by special relativity: Your spaceshiplaunches in June 2020 and returns back to Earth directly after arriving at Sirius. (c) How many years will have passed from your perspective?(d) At which Earth date (year and month) will you arrive back to Earth?arrow_forward(a) What is the number of molecules per cubic meter in air at 20C and at a pressure of 1.0 atm (= 1.01 * 10^5 Pa)? (b) What is the mass of 1.0 m3 of this air? Assume that 75% of the molecules are nitrogen (N2) and 25% are oxygen (O2).arrow_forwardA white dwarf star is essentially a degenerate electron gas, with a bunch of nuclei mixed in to balance the charge and to provide the gravitational attraction that holds the star together. In this problem you will derive a relation between the mass and the radius of a white dwarf star, modeling the star as a uniform-density sphere. White dwarf stars tend to be extremely hot by our standards; nevertheless, it is an excellent approximation in this problem to set T = O. Question is attachedarrow_forward
- A white dwarf star is essentially a degenerate electron gas, with a bunch of nuclei mixed in to balance the charge and to provide the gravitational attraction that holds the star together. In this problem you will derive a relation between the mass and the radius of a white dwarf star, modeling the star as a uniform-density sphere. White dwarf stars tend to be extremely hot by our standards; nevertheless, it is an excellent approximation in this problem to set T = O. The equilibrium radius of the white dwarf is that which minimizes the total energy Ugrav + Ukinetic. Sketch the total energy as a function of R, and find a formula for the equilibrium radius in terms of the mass. As the mass increases, does the radius increase or decrease? Does this make sense?arrow_forwardProblem 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. 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? 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 = 5.8 × 1015 m (around 6 light years)…arrow_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_forward
- The volume V of an ideal gas varies directly with the temperature T and inversely with the pressure P. If a cylinder of 50 liters contains oxygen at a temperature of 200 K and a pressure of 5 atmospheres, what would the gas pressure be if the volume was changed to 30 liters and the temperature raised to 240 K?arrow_forwardIn the hot gases of an automotive engine's cylinders, temperatures may exceed 3100 k. What would be the "root mean square" or "rms" velocity of a hydrogen atom, if one happened to be in that gas after some chemical reaction? The mass of a hydrogen atom is about 1.66x10-27 kg. Give your answer in m/s, but enter only the number.arrow_forwardCalculate the mass of an atom of (a) helium, (b) iron, and (c) lead. Give your answers in kilograms. The atomic masses of these atoms are 4.00 u, 55.9 u, and 207 u, respectively.arrow_forward
- What is the ratio of the multiplicity of water vapor at 100∘C to that of liquid water at 100∘C for 1.0 g of water at a pressure of 1.0 atm? Give your answer as a power of 10.arrow_forwardProblem 5: Any ideal gas at standard temperature and pressure (STP) has a number density (atoms per unit volume) of p = N/V = 2.68 × 1025 m²3. How many atoms are there in 11 cubic micrometers, at STP? N =| atomsarrow_forwardThe temperature inside a supernova explosion is said to be 2.00×1013 K . (a) What would the average velocity vrms of hydrogen atoms be?(b) What is unreasonable about this velocity? (c) Which premise or assumption is responsible?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