1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ludmilka [50]
3 years ago
14

When doing numerical calculations involving temperature, you need to pay particular attention to the temperature scale you are u

sing. In general, you should use the Kelvin scale (for which T = 0 represents absolute zero) in such calculations. This isbecause the standard thermodynamic equations (i.e., the ideal gaslaw and the formula for energy of a gas in terms of temperature)assume that zero degrees represents absolute zero.
If you are given temperatures measured in units other thankelvins, convert them to kelvins before plugging them into theseequations. (You may then want to convert back into the initialtemperature unit to give your answer.)
Part A) The average kinetic energy of the molecules of anideal gas at 10 ^\circ {\rm C} has the value K_10. At what temperature T_1 (in degrees Celsius) will the average kinetic energy ofthe same gas be twice this value, 2K_{10}?
Express the temperature to thenearest integer.
Part B) The molecules in an ideal gas at10 ^\circ {\rm C} have a root-mean-square (rms) speed v_rms. At what temperature T_2 (in degrees Celsius) will the molecules have twice therms speed, 2v_{\rm rms} ?
Physics
1 answer:
Mrac [35]3 years ago
8 0

1) 293 ^{\circ}C

2) 859^{\circ}C

Explanation:

1)

The average kinetic energy of the molecules of an ideal gas is directly related to the Kelvin temperature of the gas, by the formula

KE=\frac{3}{2}kT

where

KE is the kinetic energy

k is the Boltzmann constant

T is the Kelvin temperature

We can say  therefore that the average kinetic energy of the particles is directly proportional to the absolute temperature of the gas; so, we can write:

KE\propto T

And therefore

\frac{KE_1}{KE_2}=\frac{T_1}{T_2} (1)

In this problem, we have:

KE_1 = K_{10} is the initial kinetic energy of the molecules when the temperature of the gas is

T_1=10^{\circ}+273=283 K

Here we want to find the temperature T_2 at which the average kinetic energy of the particles is

KE_2=2K_{10}

So, twice the initial value. Substituting into eq.(1) and solving for T2, we find:

T_2=\frac{T_1 KE_2}{KE_1}=\frac{(283)(2K_{10})}{K_{10}}=566 K

Converting into Celsius degrees,

T_2=566-273=293 ^{\circ}C

2)

The root-mean-square (rms) speed of the molecules in a gas is given by the equation

v=\sqrt{\frac{3kT}{m}}

where

k is the Boltzmann constant

T is the Kelvin temperature of the gas

m is the mass of each molecule

Therefore, from the equation we can say that the rms speed is proportional to the square root of the temperature:

v\propto \sqrt{T}

So we can write:

\frac{v_1}{v_2}=\frac{\sqrt{T_1}}{\sqrt{T_2}} (2)

where in this problem:

v_1 = v_{rms} is the rms speed of the molecules when the temperature is

T_1=10^{\circ}C+273=283 K

v_2=2v_{rms} is the final rms speed of the molecules

Solving eq.(2), we find the temperature at which the rms speed is twice the initial value:

T_2=T_1 (\frac{v_2}{v_1})^2=(283)(\frac{2v_{rms}}{v_{rms}})^2=1132 K

Converting into Celsius degrees,

T_2=1132-273=859^{\circ}C

You might be interested in
Which of the following materials is an insulator against electric current
Leya [2.2K]

Aluminum foil (I think, it may not be right)

8 0
3 years ago
Read 2 more answers
How are light years used to measure distances in the universe
FinnZ [79.3K]
A light year is a unit of distance. It is a distance that light can travel in a years time which is six trillion miles. It is used to measure the distances in space. To take one example, the distance to the next nearest big galaxy, the Andromeda Galaxy, from earth is 21,000,000,000,000,000,000 km. 
Do you understand it? <span />
4 0
3 years ago
Given the equation p2 = a3, what is the orbital period, in days, for the planet venus? (venus is located 0.72 au from the sun?)
melisa1 [442]

The correct answer is 223 days.

The relationship between the duration of revolution and the separation between the sun is shown by Kepler's third law. Using the notions of circular motion and the gravitational and centripetal forces, we may obtain this equation.

According to Kepler's third rule, the semi-major axis of an orbit is linked to the orbital period of a planet around the sun as follows:

p² = a³

where an is the semi-major axis/distance to the star and p is the orbital period in years.

It is said that a = 0.72 AU for Venus.

P= √(0.72 AU)^3 = 0.61 years.

365 days in a year = 222.9 ≈ 223 days.

To learn more about Kepler's third rule refer the link:
brainly.com/question/1608361

#SPJ4

5 0
1 year ago
2. the dipole moment of a dipole in a 300-n/c electric field is initially perpendicular to the field, but it rotates so it is in
aleksandr82 [10.1K]

Work Done (W) by the field is-6x 107 J,

<h3>What is Electric dipole?</h3>

A pair of opposite, non-coplanar, equally powerful electric charges that are in opposition to one another. An atom is said to have a "induced electric dipole" if the center of the negative cloud of electrons has moved a little bit away from the nucleus due to an external electric field. When the external field is taken away, dipolarity is lost.

Electric field (E) = 300 N/C

Dipole moment (p) = 2 x 10° Cm

Solution:

From the formula we know.

U = -pE cosФ

Here,

p Denotes Dipole moment.

E Denotes Electric field.

Ф Denotes angle b/w them

Now, as given, firstly the dipole is perpendicular to the electric field, so

angle (Ф1) will be 90° and now the dipole is rotated such that they are in same

direction so the angle (Ф2) will be 0°

So, let's find Change in Potential energy which will be equal to the work done

by the electric field.

ΔU = Uf - Ui

ΔU = [-pE*cos Ф2] - [-pE *cos Ф1]

ΔU = [-pE*cos Ф2] + pE *cos Ф1

ΔU = pE * [cos Ф2+ cos Ф1]

Substituting the values,

ΔU = pE * [cos 0° + cos 90°]

ΔU = pE * (-1 +0)

ΔU = -pE

ΔU = -2x 10^-9 × 300

ΔU = 6 x 10^(-9+2)

ΔU = 6 x 10^-7

W = ΔU = -6 x 10^-7

W = - 6 x 10 7 J

Work Done (W) by the field is - 6 x 10-7 J.

To learn more about Work Done visit:

https://brainly.in/question/48222628

#SPJ4

6 0
2 years ago
Is an atom with one valence electron more reactive than an atom with two electrone? ​
andrey2020 [161]

Answer:

An atom with a closed shell of valence electrons (corresponding to an electron configuration s2p6) tends to be chemically inert. An atom with one or two valence electrons more than a closed shell is highly reactive, because the extra valence electrons are easily removed to form a positive ion.Explanation:

7 0
3 years ago
Other questions:
  • What do microwaves have in common with light waves?
    10·2 answers
  • Help solve these two problems im having trouble trying to start these problems?​
    8·1 answer
  • If the density of an object is 60 g/cm^3 and its mass is 20 grams, what is its volume in cm^3?
    15·1 answer
  • Please help. I need help with the questions on this page.
    10·1 answer
  • Which of these statements describes what occurs in facilitated diffusion?-Facilitated diffusion requires energy from the cell to
    6·1 answer
  • You are asked to design an experiment which is similar to Match Graph activity. If you move 3m back from the motion sensor in 2s
    15·1 answer
  • Imagine that you work for a conservation organization. Your job is to make recommendations to restore an area of a prairie that
    13·1 answer
  • 1. A 500-g block is placed on a level, frictionless surface and attached to an ideal spring. At t = 0 the block moves through th
    8·1 answer
  • If the average movement of the particles in a sweater increases, what will happen to the sweater's temperature?
    12·1 answer
  • A diamond sparkles more than a glass cut to similar shapes,why?​
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!