Modern Physics For Scientists And Engineers
2nd Edition
ISBN: 9781938787751
Author: Taylor, John R. (john Robert), Zafiratos, Chris D., Dubson, Michael Andrew
Publisher: University Science Books,
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Chapter 3, Problem 3.25P
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For an ideal gas, number density of molecules is equal to
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An ideal gas is held in a container of volume V at pressure p. The rms speed of a gas molecule under these conditions is v. If the volume and pressure are changed to 3V and 2p, what will be the rms speed of the gas molecule (compared to the original speed v)?
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?
The average translational kinetic energy for a molecule (Erans) is given
by the following equation:
Etrans =mv?
Where m is the mass of the molecule and v? is the average of the square
of the velocity. Given v2 = 3kT/m where k is the Boltzmann's constant,
calculate the ratio of the kinetic energies at 200 °C and 100 °C
Chapter 3 Solutions
Modern Physics For Scientists And Engineers
Ch. 3 - Prob. 3.1PCh. 3 - Prob. 3.2PCh. 3 - Prob. 3.3PCh. 3 - Prob. 3.4PCh. 3 - Prob. 3.5PCh. 3 - Prob. 3.6PCh. 3 - Prob. 3.7PCh. 3 - Prob. 3.8PCh. 3 - Prob. 3.9PCh. 3 - Prob. 3.10P
Ch. 3 - Prob. 3.11PCh. 3 - Prob. 3.12PCh. 3 - Prob. 3.13PCh. 3 - Prob. 3.14PCh. 3 - Prob. 3.15PCh. 3 - Prob. 3.16PCh. 3 - Prob. 3.17PCh. 3 - Prob. 3.18PCh. 3 - Prob. 3.19PCh. 3 - Prob. 3.20PCh. 3 - Prob. 3.21PCh. 3 - Prob. 3.22PCh. 3 - Prob. 3.23PCh. 3 - Prob. 3.24PCh. 3 - Prob. 3.25PCh. 3 - Prob. 3.26PCh. 3 - Prob. 3.27PCh. 3 - Prob. 3.28PCh. 3 - Prob. 3.29PCh. 3 - Prob. 3.30PCh. 3 - Prob. 3.31PCh. 3 - Prob. 3.32PCh. 3 - Prob. 3.33PCh. 3 - Prob. 3.34PCh. 3 - Prob. 3.35PCh. 3 - Prob. 3.36PCh. 3 - Prob. 3.37PCh. 3 - Prob. 3.38PCh. 3 - Prob. 3.39PCh. 3 - Prob. 3.40PCh. 3 - Prob. 3.41PCh. 3 - Prob. 3.42PCh. 3 - Prob. 3.43PCh. 3 - Prob. 3.44PCh. 3 - Prob. 3.45PCh. 3 - Prob. 3.46PCh. 3 - Prob. 3.47PCh. 3 - Prob. 3.48PCh. 3 - Prob. 3.49PCh. 3 - Prob. 3.50PCh. 3 - Prob. 3.51P
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- One mole of an ideal gas at standard temperature and pressure occupies 22.4 L (molar volume). What is the ratio of molar volume to the atomic volume of a mole of hydrogen ? (Take the size of hydrogen molecule to be about 1 Å). Why is this ratio so large ?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_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
- A gas is cooled and trapped in a two-dimensional region by laser beams and magnets. The speed distribution function of the gas molecules obeys the two-dimensional Maxwell-Boltzmann distribution law, f(v)=2π(m2πkB T)ve−mv22kB T where m is the mass of a gas molecule, T is the temperature, and v is the speed. What is the average speed of the gas molecule?arrow_forwardThe speed of a molecule in a uniform gas at equilibrium is a random variable V whose density function is given by S(0) = av²e-b*; D > 0, where b = m/(2kT) and k, T and m denote Boltzmann's constant, the absolute temperature, and the mass of the molecule, respectively. (a) Derive the distribution of W = mV² /2, the kinetic energy of the molecule. (b) Find E (W).arrow_forwardShow that the RMS velocity of gas molecule is directly proportional to square root of its absolute temperature.arrow_forward
- Assume that air is an ideal gas under a uniform gravitational field, so that the potential energy of a molecule of mass m at altitude z is mgz. Show that the distribution of molecules varies with altitude as given by the distribution function f(z) dz = Cz exp(-βmgz) dz and that the normalization constant Cz= mg/kT. This distribution is referred to as the law of atmospheres.arrow_forwardAt what temperature would the rms speed of helium atoms equal a. the escape speed from Earth, 1.12 m/s b. the escape speed from the Moon, 2.37 m/s? Note: The mass of a helium atom is 6.64 x 10-27 kg and the Boltzmann’s constant isarrow_forwardThe density of gold is 19.32g/cm^3. Do dimensional analysis to figure out how you can approximate the surface density of gold in atoms cm^−2.arrow_forward
- You are studying a gas known as "gopherine" and looking in the literature you find that someone has reported the partition function for one molecule of this gas, 5/2 AzT q(V, T) = ) %3D h?m Assume that the molecules are independent and indistinguishable. Derive the expressions for the energy, (E), for this gas. Give your answers in terms of N, kg, T. V and the constants A and B. O (E) = NkaT ㅇ (E) =D NkaT ㅇ (E) %3D NkaT- O (E) = ANKET - O (E) = - T ㅇ (E)=D 쑤-arrow_forwardWhat is the mean free path of molecules in an ideal gas in which the mean collision time is 4.00 × 10-10 s, the temperature is 294K, and the mass of the molecules is 6.00 × 10-25 kg? Assume that the molecules are moving at their root-mean-square speeds. The Boltzmann constant is 1.38 × 10-23 J/K. GIve your answer in Angstroms ( 1 Angstrom = 10-10 m)arrow_forwardThe atomic and molecular rms speeds of gases, vrms, are usually quite large, even at low temperatures. What is vrms, in meters per second, for helium atoms at 4.8 K (which is close to the point of liquefaction)? Numeric : A numeric value is expected and not an expression.vrms = __________________________________________arrow_forward
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