An constant density interstellar cloud with a radius of 2215 AU consists of an ideal gas of pure ...
Homework Answers
Total initial energy of the cloud is
Given that the initial kinetic energy Ki is 12.3 % of the initial potential energy Ui we have,
where M is the total mass and Ri is the initial radius of the gas cloud.
When it reaches equilibrium , then according to the virial theorem its final kinetic energy Kf and final potential energy Uf are related by,
Hence total final energy is
where Rf is the final radius of the gas cloud. Assuming no heat loss we must have ,
Inserting the expressions of Ei and Ef into the above equation and simplifying we obtain,
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An constant density interstellar cloud with a radius of 2215 AU consists of an ideal gas of pure ...
Learning Goal Internal Energy of an ideal gas The internal energy of a system is the...
Learning Goal Internal Energy of an ideal gas The internal energy of a system is the energy stored in the system. In an ideal gas, the internal energy includes the kinetic energies (translational and rotational) of all the molecules, and other energies due to the interactions among the molecules. The internal energy is proportional to the Absolute Temperature T and the number of moles n (or the number of molecules N). n monatomic ideal gases, the interactions among the molecules...
A satellite of mass m is in a circular orbit of radius R2 around a spherical planet of radius R1 made of a material with density ρ. ( R2 is measured from the center of the planet, not its surface.) Use G for the universal gravitational constant.
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Imagine a hypothetical star of radius R, whose mass density ρ is constant throughout the star....
Imagine a hypothetical star of radius R, whose mass density ρ is constant throughout the star. The star is composed of a classical ideal gas of ionized hydrogen, so there are free protons and free electrons flying around providing the pressure support. The star is in hydrostatic equilibrium (a) What is the pressure as a function of radius in the star, P(r)? As a boundary condition, the pressure at the surface should be zero, P(R) 0 (b) What is the...
3. A simple model of a Neutron star is an ideal gas of neutrons (each with spin 1/2 in units of h...
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The ideal gas law, discovered experimentally, is an equation of state that relates the observable state variables of the gas. pressure, temperature, and density
The ideal gas law, discovered experimentally, is an equation of state that relates the observable state variables of the gas. pressure, temperature, and density (or quantity per volume$$ \eta V=N k_{\mathrm{B}} T(\mathrm{or} p V=n \mathrm{RT}) $$Where \(N\) is the number of atoms, \(n\) is the number of moles, and \(R\) and \(k_{\mathrm{B}}\) are ideal gas constants such that \(R=N_{\mathrm{A}} k_{\mathrm{B}}\), where \(N_{A}\) is Avogadro's number. In this problem. you should use Boltzmann's constant instead of the gas constant \(R\).Remaıkably. the...
(d) 0.10 mol of an ideal gas undergoes an isothermal (constant temperature) process 1 to 2...
(d) 0.10 mol of an ideal gas undergoes an isothermal (constant temperature) process 1 to 2 as shown in the P-V diagram below. The net heat transfer (Q) during this process is: (Conversion: 1 atm = 1.013 x 10° Pa and 1 cm = 10) p (atm) 2 1 0 V(em) 1000 2000 3000 (i) 200 (ii) 334) (iii) 400 (iv) 600 (v) 230 (vi) 0J (e) Given an ideal gas which consists of only 10 atoms. Each atom has...
• A sphere of radis s as a constant volume charge density > 0 • A...
• A sphere of radis s as a constant volume charge density > 0 • A puin partide - and cro < inlevala with the electric potential AV() shown below. The particle has che or via la le right all willa velocity AV (Volts) I=0 1. (15 points) What is the eletric field inside und eutside of the chute distribution. To s you need to show WIT rulli fra exi 1. (7 points) Craph the cleetric field (r) function of...
some context Problem 3: Use simple kinetic theory of gases discussed in section 1.3.2 as well...
some context
Problem 3: Use simple kinetic theory of gases discussed in section 1.3.2 as well as Fourer's law of condustion to prove: 2 R373 D11 = 3113/202pm Dal We were unable to transcribe this imageof a nes. the xed the led negligible The following assumptions about the structure of the cases are made in order to investigate the statistical rules of the random motion of the molecules: The size of the gas molecules is negligible compared with the distance...
What is the volume of the sphere in Procedure 2 in units of cm3? Express your...
What is the volume of the sphere in Procedure 2 in units of
cm3? Express your answer to two significant figures.
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Problem 1 N molecules of carbon dioxide gas Co, (considered as an ideal gas) undergo the...
Problem 1 N molecules of carbon dioxide gas Co, (considered as an ideal gas) undergo the cycle shown in the P-V diagram on the right. As a reminder, a CO, molecule has all atoms on a line. Assume that all processes are quasistatic and that the temperature remains such that rotational degrees of freedom are activated, but vibrational degrees of freedom are frozen out. Capital letters A, B, C represent the states at the corners of the cycle, while lowercase...
Learning Goal Internal Energy of an ideal gas The internal energy of a system is the energy stored in the system. In an ideal gas, the internal energy includes the kinetic energies (translational and rotational) of all the molecules, and other energies due to the interactions among the molecules. The internal energy is proportional to the Absolute Temperature T and the number of moles n (or the number of molecules N). n monatomic ideal gases, the interactions among the molecules...
Imagine a hypothetical star of radius R, whose mass density ρ is constant throughout the star. The star is composed of a classical ideal gas of ionized hydrogen, so there are free protons and free electrons flying around providing the pressure support. The star is in hydrostatic equilibrium (a) What is the pressure as a function of radius in the star, P(r)? As a boundary condition, the pressure at the surface should be zero, P(R) 0 (b) What is the...
3. A simple model of a Neutron star is an ideal gas of neutrons (each with spin 1/2 in units of h). Aside from the kinetic energy of the neutrons, one must consider the gravitational energy, which for a homogeneous star of mass M and radius R, is 3GM2 5R where G 6.67 x 10-11m3kg-'s-2 is the universal gravitational constant (i) We suppose in this problem that the Fermi temperature is large enough for T0 What general condition determines the...
The ideal gas law, discovered experimentally, is an equation of state that relates the observable state variables of the gas. pressure, temperature, and density (or quantity per volume$$ \eta V=N k_{\mathrm{B}} T(\mathrm{or} p V=n \mathrm{RT}) $$Where \(N\) is the number of atoms, \(n\) is the number of moles, and \(R\) and \(k_{\mathrm{B}}\) are ideal gas constants such that \(R=N_{\mathrm{A}} k_{\mathrm{B}}\), where \(N_{A}\) is Avogadro's number. In this problem. you should use Boltzmann's constant instead of the gas constant \(R\).Remaıkably. the...
(d) 0.10 mol of an ideal gas undergoes an isothermal (constant temperature) process 1 to 2 as shown in the P-V diagram below. The net heat transfer (Q) during this process is: (Conversion: 1 atm = 1.013 x 10° Pa and 1 cm = 10) p (atm) 2 1 0 V(em) 1000 2000 3000 (i) 200 (ii) 334) (iii) 400 (iv) 600 (v) 230 (vi) 0J (e) Given an ideal gas which consists of only 10 atoms. Each atom has...
• A sphere of radis s as a constant volume charge density > 0 • A puin partide - and cro < inlevala with the electric potential AV() shown below. The particle has che or via la le right all willa velocity AV (Volts) I=0 1. (15 points) What is the eletric field inside und eutside of the chute distribution. To s you need to show WIT rulli fra exi 1. (7 points) Craph the cleetric field (r) function of...
some context
Problem 3: Use simple kinetic theory of gases discussed in section 1.3.2 as well as Fourer's law of condustion to prove: 2 R373 D11 = 3113/202pm Dal We were unable to transcribe this imageof a nes. the xed the led negligible The following assumptions about the structure of the cases are made in order to investigate the statistical rules of the random motion of the molecules: The size of the gas molecules is negligible compared with the distance...
What is the volume of the sphere in Procedure 2 in units of
cm3? Express your answer to two significant figures.
LAB 14: IDEAL GAS LAW BASIC CONCEPTS TEXTBOOK: SECTIONS 15.2, YOUNG, 10TH EDITION DEFINITIONS Volume: The space taken up by an object, measured in cubic meters (m"). Pressure: For an enclosed gas, pressure is defined as the force exerted per area by the gas on the container walls, measured in Pascal (1 N/m) Temperature: A measure of the average...
Problem 1 N molecules of carbon dioxide gas Co, (considered as an ideal gas) undergo the cycle shown in the P-V diagram on the right. As a reminder, a CO, molecule has all atoms on a line. Assume that all processes are quasistatic and that the temperature remains such that rotational degrees of freedom are activated, but vibrational degrees of freedom are frozen out. Capital letters A, B, C represent the states at the corners of the cycle, while lowercase...
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