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Chapter 19: Q21P (page 578)

Question: The lowest possible temperature in outer space is 2.7 K. What is the rms speed of hydrogen molecules at this temperature? (The molar mass is $2.02 脳 10^{- 3} k g / m o l$ ).

Short Answer

Expert verified

Answer:

The RMS speed of the hydrogen molecules is $1.8 脳 10^{2} m / s$ .

Step by step solution

01

Given data

The temperature is T = 2.7 K

The molar mass of hydrogen molecules is, $M = 2.02 脳 10^{- 3} k g / m o l$

02

Concept introduction

We can find the rms speed using its formula in terms of R, temperature, and molar mass.

The expression for the RMS speed is given by,

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

03

Calculate the rms speed of hydrogen molecules at the given temperature

The RMS speed of hydrogen molecules is

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

Molar mass of hydrogen is $M = 2.02 脳 10^{- 3} k g / m o l$

$v = \sqrt{\frac{3 (8.314) (2.7)}{2.02 脳 10^{- 3}}} v = 182.58 鈮� 1.8 脳 10^{2} m / s$

Therefore the RMS speed of the hydrogen molecules is $1.8 脳 10^{2} m / s$ .

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Most popular questions from this chapter

Question: An air bubble of volume 20 cm³is at the bottom of a lake 40 mdeep, where the temperature is 4. 0 ⁰C. The bubble rises to the surface, which is at a temperature of. Take the temperature of 20 ⁰C the bubble鈥檚 air to be the same as that of the surrounding water. Just as the bubble reaches the surface, what is its volume?

Water standing in the open at $32.0 掳 C$ evaporates because of the escape of some of the surface molecules. The heat of vaporization () is approximately equal to $蔚 n$ , where $蔚$ is the average energy of the escaping molecules and is the number of molecules per gram.

Find $蔚$
What is the ratio of $蔚$ to the average kinetic energy of $H_{2} O$ molecules, assuming the latter is related to temperature in the same way as it is for gases?

The dot in Figre 19-18bpresents the initial state of a gas, and the isotherm through the dot divides the p-V diagram into regions 1 and 2. For the following processes, determine whether the change ${螖贰}_{i n t}$ in the internal energy of the gas is positive, negative, or zero: (a) the gas moves up along the isotherm, (b) it moves down along the isotherm, (c) it moves to anywhere in region, and (d) it moves to anywhere in region.

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?

At $20 掳 C$ and $750 t o r r$ pressure, the mean free paths for argon gas (Ar) and nitrogen gas ( $N_{2}$ ) ARE $位_{A r} = 9.9 脳 10^{- 6} c m$ and $位_{N 2} = 27.5 脳 10^{- 6} 鈥� c m$ .

a) Find the ratio of the diameter of $A_{r}$ an atom to that of an $N_{2}$ molecule.

b) What is the mean free path of argon at $20 掳 C$ and $150 t o r r$ ?

c) What is the mean free path of argon at $- 40 掳 C$ and $750 t o r r$ ?

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