The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol R or R. It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per mole, i.e. the pressure–volume product, rather than energy per temperature increment per particle. The constant is also a combination of the constants from Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. It is a physical constant that is featured in many fundamental equations in the physical sciences, such as the ideal gas law, the Arrhenius equation, and the Nernst equation.
The gas constant is the constant of proportionality that relates the energy scale in physics to the temperature scale and the scale used for amount of substance. Thus, the value of the gas constant ultimately derives from historical decisions and accidents in the setting of units of energy, temperature and amount of substance. The Boltzmann constant and the Avogadro constant were similarly determined, which separately relate energy to temperature and particle count to amount of substance.
The gas constant R is defined as the Avogadro constant NA multiplied by the Boltzmann constant k (or kB):
R
=
N
A
k
.
{\displaystyle R=N_{\rm {A}}k.}
Since the 2019 redefinition of SI base units, both NA and k are defined with exact numerical values when expressed in SI units. As a consequence, the SI value of the molar gas constant is exactly 8.31446261815324 J⋅K−1⋅mol−1.
Some have suggested that it might be appropriate to name the symbol R the Regnault constant in honour of the French chemist Henri Victor Regnault, whose accurate experimental data were used to calculate the early value of the constant. However, the origin of the letter R to represent the constant is elusive. The universal gas constant was apparently introduced independently by Clausius’ student, A.F. Horstmann (1873)
and Dmitri Mendeleev who reported it first on Sep. 12, 1874.
Using his extensive measurements of the properties of gases,
he also calculated it with high precision, within 0.3% of its modern value.
The gas constant occurs in the ideal gas law:
P
V
=
n
R
T
=
m
R
s
p
e
c
i
f
i
c
T
{\displaystyle PV=nRT=mR_{\rm {specific}}T}
where P is the absolute pressure (SI unit pascals), V is the volume of gas (SI unit cubic metres), n is the amount of gas (SI unit moles), m is the mass (SI unit kilograms) contained in V, and T is the thermodynamic temperature (SI unit kelvins). Rspecific is the mass-specific gas constant. The gas constant is expressed in the same units as are molar entropy and molar heat capacity.
Homework Statement
a)Helium enters a closed system as a flow of compressed gas at a temperature
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Homework Statement
Not sure if the link is showing. But it's imgur.com/a/LEvd0
Homework Equations
The steps I've taken so far as written in the attempt section below is correct.
The solution provided then proceeds with letting ##z = x + iy## and setting ##\ddot z+i \omega \dot z = 0##. Then...
Homework Statement
Having a conducting sphere with radius ##R## and charge ##Q##, dielectric is put on it so that a spherical shell with inner radius ##R## and outer radius ##3R## is formed. Calculate:
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If we have a medium (say, glass) with an index of refraction, n=1.33, the speed of light in it will be c/1.33. However, blue light travels slower in glass than does red light. Since c is constant and the speed of light is changing, doesn't that mean that the index of refraction will vary based...
Homework Statement
[/B]
The block, initially at rest, slides down the ramp and compresses the spring 0.03 m.
Theta = 30 degrees
L = 1.25 m
M of block = 2 kg
Δx = 0.03 m
1) Write the expression for the initial and final energy states
2) Find the spring constant K
Homework Equations
mgh...
Hey!
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Homework Statement
Consider a conducting sphere with radius ##R## connected to a voltage source of ##V_0## volts. If the sphere is then covered by a dielectric spherical layer of radius ##9R## calculated the relative permitivitty ##\varepsilon_0## needed so that the field in the empty zone...
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Homework Statement
Spring Compressed = 20cm = .2m
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Homework Equations
k = fx
The Attempt at a Solution
I have no idea where to go from here...
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The mystery of 0.577
4k1jegU4Wb4
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Homework Statement
decreasing the resistance increases the current if the voltage remains unchanged.
Homework Equations
V=IR
The Attempt at a Solution
The solution in the book does not count this as a true statement, but it seems true to me. Is there any reason why the statement would be false?
Homework Statement
African baobab trees can have circumferences of up to 43.0 m. Imagine riding a bicycle around a
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Homework Statement
A loaded railroad car is rolling at a constant velocity when it couples with a spring and dashpot
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Homework Statement
Force of jet= A(r(t))4/3
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Griffith's Introduction to Elementary Particles, if I understand it correctly, states that in QED, the fine structure constant contributes less and less to the strength of the EM interaction as we add more and more vertices since the constant is so small (1/137). However, in QCD, since the...
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Hello, this is my first post. I need to solve some problems for my class, and I got stuck with this one.
The problem (this is a translation):
Your father has just turned 50 (t = 0) and wants to retire in 15 years (t = 15). He thinks he will live 25 years after retirement, until he is 90 years...
Hello all,
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Homework Statement
Hi. I started studying LR circuits and the first thing that made me do searches in textbooks of mine and in the internet was the time constant which is surprisingly not L times R, but L/R which would mean the time needed to store and release energy is being prolonged with...
Homework Statement
A plane, diving with constant speed at an angle of 53 degrees with the vertical, releases a projectile an altitude of 730m. The projectile hits the ground 5.00s after release. A plane, diving with constant speed at an angle of 53 degrees with the vertical, releases a...
Homework Statement
N2 + 3H2 --> 2NH3 (all gases)
Why is such a high pressure needed? Calculate the equilibrium constant at 500k then estimate the percentage conversion at equilibrium at 1 bar total pressure, assuming the stoichiometric ratio of N2:H2 is 1:3.
Repeat the process at 50 bar...
Homework Statement
A rocket is flying away from the Earth with a costant acceleration ##a## in a frame in which the rocket is at rest. Finding the equation of motion (the relation between the distance from the Earth and the terrestrial time). Showing that there is a maximum time ##T## after the...
Homework Statement
Homework Equations
Time constant = 1/ξwn
The Attempt at a Solution
Time constant = 1/ξwn
Damping factor = ξwn
So T = 1/ξwn
If ξwn is reduced by factor of 2, then Time constant must be increased by factor of 2.
So Answer is: B
Book answer is A
How?
p.s. I know I'm posting...
Homework Statement
Homework Equations
Express denominator as 1 + sT1
The Attempt at a Solution
In denominator
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s + 3 can be written as: 3(1 + 0.3s)
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Why are the fundamental physical constants called "constants" when they change over time?
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Homework Statement
I need to calculate a spring constant using measurements from a Hooke's Law Apparatus, a spring, and some weights. The weights are hung vertically from the spring and the distance is measured from the equilibrium point of the spring. If I'm solving for k, then k=F/x. I do...
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Homework Statement
[/B]
An X-ray tube gives electrons constant acceleration over a distance of 14 cm . If their final speed is 1.0×107 m/s , what are the electrons' acceleration?
Express your answer to two significant figures and include the appropriate units.
Homework Equations
My prof. has...
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Homework Statement
14.27 The 2.5-kg weight is released from rest in position A, where the two springs
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Homework EquationsThe Attempt at a Solution
Hi. Can you check if I am going at...
Homework Statement
Show that the normalized wave function for a particle in a three-dimensional box with sides of length a, b, and c is:
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Homework Equations
Condition for the normalization:
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An antelope moving with constant acceleration covers the
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The answer to this is 5 m/s
ok this should be real simple but...
Homework Statement
Homework Equations
I know for RL circuit T = L/R
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I calculated for RL as 1/4 = 0.25
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In...
Homework Statement
A particle is restrained to move in 1D between two rigid walls localized in ##x=0## and ##x=a##. For ##t=0##, it’s described by:
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Homework Statement
An object of mass 100kg is acted on by a constant force as it moves through a displacement at a constant speed of 7.2m/s. What is the net work done on the object?
Homework Equations
Wnet = ΔK
Fnet = 0
The Attempt at a Solution
I know that the answer is zero because the...
Homework Statement
Homework Equations
d = vit + 1/2at^2
The Attempt at a Solution
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Hi.
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I am having problem on understanding the below solution regarding constant of integration.
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Hello. I've been watching Susskind's online Stanford lectures on classical mechanics to review the subject, and I believe he said that adding a constant to the potential energy does not change the action of a system. I see how it doesn't change the Euler-Lagrange equations and therefore...
$\tiny{243.13.01.19}$
$\textsf{The following equations each describe the motion of a particle.}$
$\textsf{ For which path is the particle's speed constant?}$
\begin{align*} \displaystyle
R_1(t)&= t^7\textbf{i}+t^4\textbf{j}\\
R_2(t)&= \cos(3t)\textbf{i}+\sin(8t)\textbf{j}\\
R_3(t)&=...
Does the presence of the cosmological constant modify the rate of expansion of the universe even during the earlier deceleratingly expanding phase of the universe?
Homework Statement
I am stuck on finding ##W^u##
Homework Equations
[/B]
I have computed the christoffel symbols via comparing the Euler-Lagrange equations to the form expected from geodesic equation.
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