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.
What I tried to do was using the fact that the wave function should be continuous.
Asin(kb)=Be^{-\alpha b}
The derivative also should be continuous:
kAcos(kb)=-\alpha Be^{-\alpha b}
And the probability to find the particle in total should be 1:
\int_0^b A^2sin^2(kx) dx + \int_b^{\infty}...
Could someone please help me understand why ##h## isn't known as Wien's constant?
In his "approximation":
it just looks like he used the wrong distribution function (Maxwell-Boltzmann) with ##h\nu## correctly for energy
And why is the correct distribution function
$$ \frac 1 {e^{\frac E...
for example, I want to know velocity of a person when time is equal to t, that person start running from 0m/s (t=0s) to max velocity of 1m/s (t=1s). I am thinking that this is like rain droplet that affected by gravity and drag force, where force is directly proportional to its velocity, to make...
I am not getting any ideas to solve this without the universal constants. The method that I want to use invloves the speed of light, which is a universal constant.
Is the below Displacement time graph posible?
if an object is in motion at a constant velocity, is it possible for it to stop instantaneously, or does there have to be a decelaration?
According to Newton's first, an object will remain in its state of constant velocity unless acted upon by...
My questions is:
Depending on which metric you choose "east coast" or "west coast", do you have to also mind the sign on the cosmological constant in the Einstein field equations?
R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu} \pm \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}
For example, if you...
I’m obviously looking at this the wrong way but…..with reference to the formula e = mc2 isn’t “c” (the speed of light) a constant? So if that is true doesn’t c2 (or any other multiple of c) equal c?
https://www.physicsforums.com/threads/what-are-the-best-parameters-for-lcdm.831858/
Hello.
In the above linked thread from 2015 Science Advisor Chalnoth replies to Earnest Guest.
First, the cosmological constant has been a component of General Relativity pretty much from the start. The way...
In my book it has the following example,
A particle confined to the surface of a sphere is in the state
$$\Psi(\theta, \phi)= \Bigg\{^{N(\frac{\pi^2}{4}-\theta^2), \ 0 < \theta < \frac{\pi}{2}}_{0, \ \frac{\pi}{2} < \theta < \pi}$$
and they determined the normalization constant for ##N##...
Visualize the following scenario. A star such as the sun, and a planet such as Earth are located in a solar system. A photon travels from sun (x0) to Earth (x1), and a satellite is in the midway observing the photon. This is relates to Einstein's special relativity.
I ask this since it take...
Now this is how I've tried to solve this
$$ v_e = u0 \cdot ln \frac {M} {M- μ \cdot t} $$
After putting in the values I get this;
$$ v_e = 200 * ln 0,36 $$
$$ v_e = 73,54 \frac m s $$
Now I'd say that this is the correct way to do it, but this part is confusing me "What is the speed of the...
In the ch1 if solid state physics Mermin & Ashcroft, in the hall effect section these paragraph are about cyclotron frequency, but what the two last terms want to say(the screen shot of the page is attached)? And I can't understand what happens to hall constant in high-field regime?
So, the only thing which came to my mind in order to solve this problem was actually to write down the equations using the discharge function, being given two instants and their corresponding charges... but doing so I'm unable to find anything.
Ideally, I'd say I should find the time constant...
Hi,
If we multiply $En=-\frac{2\pi^2me^4Z^2}{ n^2h^2} $by $\frac{1}{(4\pi\epsilon_0)^2},$ it is the formula of electron energy in nth Bohr’s orbit. Why we should multiply it by $\frac{1}{ (4\pi\epsilon_0)^2}$ a Coulomb's constant in electrostatic force?
Where m=mass of electron, e= charge...
For an ionic lattice, the contribution to the electric potential energy from a single ion will be ##U_i = \sum_{j\neq i} U_{ij}##, which can be expressed as$$\begin{align*}U_i &= -6 \left( \frac{z_+ z_- e^2}{4\pi \varepsilon_0 r_0} \right) + 12 \left( \frac{z_+ z_- e^2}{4\pi \varepsilon_0...
The principal equilibrium in a solution of NaHCO3 is
HCO3-(aq) + HCO3-(aq) <-> H2CO3(aq) + CO32-(aq)
Calculate the value of the equilibrium constant for this reaction.
My solution:
This overall reaction is the same as the sum of the following reactions:
HCO3-(aq) <-> H2CO3(aq) + OH-(aq)...
Multipart question:
1) How long would it take to travel to the moon from Earth at a constant 1 g acceleration?
2) How does fuel consumption work with constant 1 g acceleration or acceleration in general? I read that "it doesn't take a constant amount of energy to maintain a constant...
My first attempt was using the period equation of a spring system.
I've changed it into k=((2π)^2*m)/T^2, then put Earth's mass into "m" (5.972*10^24), then put the time required for one revolution of Earth around the Sun, 365 days into seconds, 31536000 sec, to "T"
So I got (2.371*10^11 kg/s^2)...
Say that we have an instance where something falls down from a certain height with constant acceleration g. We know that the average speed with regards to the time period is less than (u+v)/2 since we spend less time at the higher speeds.
How do we actually calculate the average speed over a...
We need to find the normal modes of this system:
Well, this system is a little easy to deal when we put it in a system and solve the system... That's not what i want to do, i want to try my direct matrix methods.
We have springs with stiffness k1,k2,k3,k4 respectively, and block mass m1, m2...
I am still rather new to renormalising QFT, still using the cut-off scheme with counterterms, and have only looked at the ##\varphi^4## model to one loop order (in 4D). In that case, I can renormalise with a counterterm to the one-loop four-point 1PI diagram at a certain energy scale. I can...
Approaching for the first time to these "higher level" topics is mind-blowing, and indeed I cannot understand why is the speed of light a constant... why doesn't it vary relatively to the emitter state of motion? And isn't it affected by gravity(I know it is affected in the sense of a spacetime...
The question was:
I will also include the solution:
So, what is the justification of the first formula [ω=√(C/I)]? I know how to derive simple harmonic equations, this one as I guess is probably similar? But I cannot connect as to how C is used exactly.
And the second formula [ω'=ωβ], I...
Basically I just want to work out a constant acceleration problem in relativity, of the same kind of introductory physics.
Vo= 0.9999c
Vf = 0
D= 50 Au
Accel, Earth frame?
Accel, Ship frame?
Time of transit, Earth frame?
Time of transit, ship frame?
Motion is 1-D. All origins line up at the...
This is my scope of the question, i could think to solve it by two steps, but before, let's give name to the things.
X is positive down direction.
X = 0 at the initial position o the platform
Mass of the falling block is m1
Mass of the platform, m2
Spring constant k
Δx is the initial stretched...
Wikipedia defines the derivative of a scalar field, at a point, as the cotangent vector of the field at that point.
In particular;
The gradient is closely related to the derivative, but it is not itself a derivative: the value of the gradient at a point is a tangent vector – a vector at each...
Hi, what I've done so far is solving equation 2) for ##U##, and replacing what I get in equation 1).
Then, ##c_V## is equal to the partial derivative of ##S## with respect to T times T, so I've done that. The derivative is ##CNR/T##, so ##c_V=CNR## but those aren't the correct units for ##c_V##.
History & evidence can be found in:
https://onlinelibrary.wiley.com/doi/full/10.1002/andp.201900013
https://phys.org/news/2015-04-gravitational-constant-vary.html
{unacceptable reference deleted}
The experimental data strongly suggest are actual x,y,z,t variations in the measured value of G
There's a constant magnetic field B. If a particle is acted on by a force qv*B (* cross) only, and the initial velocity v0 is normal to B, is the motion certainly a circular one (for any m, q, v0)?
mv''=qv*B
If one solves this equation (vector), it doesn't seem obvious.
Let $a,\,b,\,c,\,d,\,e,\,f$ be real numbers such that the polynomial $P(x)=x^8-4x^7+7x^6+ax^5+bx^4+cx^3+dx^2+ex+f$ factorizes into eight linear factors $x-x_i$ with $x_i>0$ for $i=1,\,2,\,\cdots,\,8$.
Determine all possible values of $f$.
The solutions start from the fact that c_v= (dT/dV)_s = -[(du/dv)_T + P], however I cannot reason where did that come from. Any help will be appreciated.
Let:
Smaller block = m1 = 1 kg
Large block = m2 = 2 kg
Coefficient of friction between the two blocks = μ1 = 0.2
Coefficient of friction between larger block and floor = μ2 = 0.3
Tension connecting two blocks through two pulleys = T
Angle between tension and horizontal = θ = 37o
Friction between...
If anybody has studied the book:
A First course in String Theory - Barton Zweibach - 2nd edition
This statement is present in 6th chapter of book on pg 110
So, when I try to solve for expansion work, I don't know nothing about Pext. I've seen multiple times that they just replace Pext with Pint but I don't really get why. I thought about a few situations and I'd like for you to correct me if I'm wrong.
If the system in vaccum: the simplest one...
Completely new to this and wondered if someone can explain what the correct equation of motion is if x is extension, t is time and a,b are constants
x = b log (at)
x = a t exp(-b t)
x = exp(-b t) sin(a t)
x = a sin(t)/b
##x^2(3x^2+4x-12) +k=0##
##(3x^2+4x-12)= \frac{-k}{x^2}##
or
##(4x^3-12x^2)=-k-3x^4##
##4(3x^2-x^3)=3x^4+k##
##4x^2(3-x)= 3x^4+k##
or using turning points,
let ##f(x)= 3x^4+4x^3-12x^2+k##
it follows that,
##f'(x)=12x^3+12x^2-24x=0##
##12x(x^2+x-2)=0##
##12x(x-1)(x+2)=0## the turning points...
I've worked through it doing what I thought I should have done. I normalized the original wavefunction(x,0) and made it = one before using orthonormality to get to A^2(1-1) because i^2=-1 but my final answer comes out at 1/0 which is undefined and I don't see how that could be correct since A is...
For a double integral, we might treat the "inner integral" separately and be able to compute something like ##\int_{x_1}^{x_2} f(x,y) dx## by holding ##y## constant during the integration. The same technique is applied in other places too, like for solving exact differential equations. I haven't...
Hi All,
I'm doing research in magnetic nanoparticles that are coated with chain molecules (oleic acid, I believe) and I am trying to model these molecules' effective spring constant.
The basic scenario is this: When a water-based ferrofluid is evaporated, it leaves behind only dried...
I know the amazing thought experiment by Albert Einstein with the two light clocks.
(The observer at the train station has a light clock and the person in the train.)
It's amazing because you can even deduce the formula to calculate how fast the clock in the train goes.
But this experiment...
Hello folks,
I am working on Java program just for fun to model an n-body problem using 3-dimension graphics. I'm looking for a way to speed up the model.
Suppose for example that I decide to increase the speeds of all objects by a factor of, say, 2. To compensate, I would also increase the...
Hello folks,
Not strictly a homework question, but thought this might be the best place for it.
If I determine (experimentally) two values for some constant k, is there a simple meaningful way to state their (percentage) agreement. For example, imagine I carry out two different experiments and...
i. the threshold frequency;
3.9x10^14hz? it appears the line intersects at 3.9ii. the work function of the surface;
6.626x10^-34x3.9x10^14= 2.58414 × 10^-19J
iii. Planck's constant
unsure
Summary:: not constant spin
How could I calculate the system lagrangian in function of the generalised coordinates and the conserved quantities associated to the system symmetries?
I've been struggling for the case with not constant angular velocity, but I don't realize what I have to do...
I'm watching this video to which discusses how to find the domain of the self-adjoint operator for momentum on a closed interval.
At moment 46:46 minutes above we consider the constant function 1
$$f:[0,2\pi] \to \mathbb{C}$$
$$f(x)=1$$
The question is that:
How can we show that the...