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Chapter 19: Q18P (page 578)

Question: The temperature and pressure in the Sun鈥檚 atmosphere are $2.00 脳 10^{6} K$ and 0.0300 paCalculate the rms speed of free electrons (mass $9.11 脳 10^{- 31} kg$ ) there, assuming they are an ideal gas.

Short Answer

Expert verified

Answer

The rms speed of free electrons is $9.53 脳 10^{6} \frac{m}{s}$ .

Step by step solution

01

Given

$T = 2.00 脳 10^{6} K, p = 0.0300 Pa, m = 9.11 脳 10^{- 31} kg$

02

Determine the concept

Find the RMS speed using the formula for root-mean-square speed. MS speed is defined as the square root of the mean of the square of speeds of all molecules.

Formula is as follow:

$v = \sqrt{\frac{3 R T}{M}}$

Here, M is mass, Tis temperature, v is velocity and R is universal gas constant.

03

Determine the rms speed of free electrons

The rms speed of electrons is,

$v = \sqrt{\frac{3 R T}{M}} M = m N_{A} a n d R = k N_{A} v = \sqrt{\frac{3 k N_{A} T}{m N_{A}}} 鈭� v = \sqrt{\frac{3 k T}{m}}$

Substitute the values and solve as:

$鈭� v = \sqrt{\frac{3 (1.38 脳 10^{- 23}) 2.00 脳 10^{6}}{9.11 脳 10^{- 31}}} v = 9.533 脳 10^{6} v = 9.53 脳 10^{6} \frac{m}{s}$

Hence, the rms speed of free electrons is $v = 9.53 脳 10^{6} \frac{m}{s}$ .

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Most popular questions from this chapter

A hydrogen molecule (diameter $1.0 脳 10^{- 8} c m$ ), travelling at the rms speed, escapes from a $4000 鈥� K$ furnace into a chamber containing $cold$ argon atoms (diameter) at a density of.

a) What is the speed of the hydrogen molecule?

b) If it collides with an argon atom, what is the closest their centres can be, considering each as spherical?

c) What is the initial number of collisions per second experienced by the hydrogen molecule? (Hint: Assume that the argon atoms are stationary. Then the mean free path of the hydrogen molecule is given by

Mean free path $= \frac{1}{蟺 d^{2} 鈥� N / V}$

Question: For air near 0 ⁰C, by how much does the speed of sound increase for each increase in air temperature by 1 ⁰C? (Hint: See Problem 91)

In a bottle of champagne, the pocket of gas (primarily carbon dioxide) between the liquid and the cork is at a pressure of $p_{1} = 5.00 鈥� a t m$ .When the cork is pulled from the bottle, the gas undergoes an adiabatic expansion until its pressure matches the ambient air pressure of $1.00 鈥� a t m$ .Assume that the ratio of the molar specific heats is $纬 = 4 / 3$ . If the gas has initial temperature $T_{i} = 5.00 掳 C$ , what is the temperature at the end of the adiabatic expansion?

Question: The speed of sound in different gases at a certain temperature T depends on the molar mass of the gases. Show that $\frac{v_{1}}{v_{2}} = \sqrt{\frac{M_{2}}{M_{1}}}$ whereis the speed of sound in a gas of molar mass M₁and v₂is the speed of sound in a gas of molar mass M₂.(Hint: See Problem 91.)

The envelope and basket of a hot-air balloon have a combined weight of $2 .45 鈥塳狈$ , and the envelope has a capacity (volume) of $2.18 脳 10^{3} m^{3}$ . When it is fully inflated, what should be the temperature of the enclosed air to give the balloon a lifting capacity (force) of $2 .67 kN$ (in addition to the balloon鈥檚 weight)? Assume that the surrounding air, at ${20.0}^{0} C$ , has a weight per unit volume of ${11.9N/m}^{3}$ and a molecular mass of $0 .028 kg/mol$ , and is at a pressure of $1.0atm$ .

See all solutions

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