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Chapter 20: Q. 19 (page 567)

By what factor does the $r m s$ speed of a molecule change if the temperature is increased from $10 ° C$ to $1000 ° C$ ?

Short Answer

Expert verified

The $r m s$ speed on the temperature is $2.12$

Step by step solution

01

Explanation

Let us remember that the formula giving the dependence of the $r m s$ speed on the temperature is

localid="1648397843905" $v_{r m s} = \sqrt{\frac{3 k_{B} T}{m}} = C \sqrt{T}$

where $C$ is a constant. Therefore, considering two $r m s$ speeds and $v_{1}$ $v_{2}$ , we have

$\frac{v_{2}}{v_{1}} = \frac{C \sqrt{T_{2}}}{C \sqrt{T_{1}}} = \sqrt{\frac{T_{2}}{T_{1}}}$

02

The rate of temperature

Keep in mind that the temperatures must be expressed in degrees Kelvin, which means that they must be $10 + 273 = 283 K$ and $1000 + 273 = 1273 K$

Substitute the value in formula

$\frac{v_{2}}{v_{1}} = \sqrt{\frac{1273}{283}}$

$= 2.12$

The heat is moving at a rate of $2.12$

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Most popular questions from this chapter

The rms speed of the molecules in $1.0 g$ of hydrogen gas is $1800 \frac{m}{s}$ .
a. What is the total translational kinetic energy of the gas molecules?
b. What is the thermal energy of the gas?
c. $500 J$ of work are done to compress the gas while, in the same process, $1200 J$ of heat energy are transferred from the gas to the environment. Afterward, what in the rms speed of the molecules?

A monatomic gas and a diatomic gas have equal numbers of moles and equal temperatures. Both are heated at constant pressure until their volume doubles. What is the ratio $Q_{d i a t o m i c} / Q_{m o n a t o m i c}$ ?

A cylinder contains gas at a pressure of $2.0 a t m$ and a number density of $4.2 \times 10^{25} m^{- 3}$ . The rms speed of the atoms is $660 m / s$ . Identify the gas.

On earth, STP is based on the average atmospheric pressure at the surface and on a phase change of water that occurs at an easily produced temperature, being only slightly cooler than the average air temperature. The atmosphere of Venus is almost entirely carbon dioxide $({CO}_{2})$ , the pressure at the surface is a staggering $93 atm$ , and the average temperature is localid="1648638013375" $470 ° C$ . Venusian scientists, if they existed, would certainly use the surface pressure as part of their definition of STP. To complete the definition, they would seek a phase change that occurs near the average temperature. Conveniently, the melting point of the element tellurium is localid="1648638019185" $450 ° C$ . What are (a) the rms speed and (b) the mean free path of carbon dioxide molecules at Venusian STP based on this phase change in tellurium? The radius of a ${CO}_{2}$ molecule islocalid="1648638027654" $1.5 \times 10^{- 10} m$ .

Integrated circuits are manufactured in vacuum chambers in which the air pressure is $1.0 \times 10^{- 10} mm$ of $Hg$ . What are (a) the number density and (b) the mean free path of a molecule? Assume $T = 20 ° C$ .

See all solutions

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