What is Constant a: Definition and 25 Discussions

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):





{\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:





{\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.

View More On Wikipedia.org
  1. A

    I Is the Hubble constant a constant or is it a parameter?

    (P.S! this is an open question, feel free to answer)
  2. S

    Normalization constant A of a harmonic oscillator

    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...
  3. Alexanddros81

    A toy car is set rolling on a straight track

    Hi. My question is regarding toy car A. If the car moves to the left, is the constant acceleration of ##2.40 \frac {cm} {s^2}## to the left or to the right?
  4. Alexanddros81

    A jet comes in for a landing on solid ground

    Homework Statement A jet comes in for a landing on solid ground with a speed of 100m/s, and its acceleration can have a maximum magnitude of ##5.00m/s^2 ## as it comes to rest. (a) From the instant the jet touches the runway, what is the minimum time interval needed before it can come to rest...
  5. opus

    Why is the universal gas constant a constant?

    The ideal gas law is given as ##PV=nRT## where ##R## is said to be the universal gas constant equal to ##0.082056\frac{L⋅atm}{mol⋅K}##. ##R## is said to be a constant, and thus cannot change even if we change the values of ##P,V,n,T##. I don't see how this is possible, because the way we found...
  6. Drakkith

    I When is a Constant a Solution to a Differential Equation

    I've run across several instances while doing homework where a question will have two solutions. One will be an equation, and the 2nd will be a constant (usually zero). I can't figure out why this constant is a solution though. For example, take the following differential equation...
  7. A

    Forces, 3 masses, 2 by Tension, constant A

    Hello, This is an advanced forces problem from introductory Calculus with Physics. I have mostly solved the problem I am posting here but am just missing a force on my diagram somewhere. M. The jpeg below "MassCartTheProblem_1.jpg" shows a picture of the situation and the goal is to find the...
  8. M

    MHB Finding the Constant a for a Given Point on a Linear Equation

    You are given an equation and a point. In each case, find the value of the constant a so that the graph of the equation passes through the given point. y = -5x - a; (-4, 1) Solution: Let x = -4 and y = 1 y = -5x - a 1 = -5(-4) - a 1 = 20 - a 1 - 20 = - a -19 = -a -19/-1 = a 19 = a...
  9. Demystifier

    A Why isn't cosmological constant a mass of the graviton?

    The Lagrangian density for cosmological constant is $${\cal L} = \sqrt{g}\Lambda$$ Let us write, schematically, $$g=\eta+h$$ where ##\eta## is the flat Minkowski metric and ##h## is the spin-2 field. Expanding the square root for small ##h## we get something like $${\cal L} = \Lambda + h\Lambda...
  10. kidgt23

    Forces of motion, Newton 2nd law

    Homework Statement An 8.5 gram slug is fired East from a 0.357 magnum hand gun held 1.5 meters above the ground. The muzzle velocity (as the projectile leaves the gun) is 1400 ft/sec. The bullet is accelerated at a constant rate as it travels through the 10 cm long barrel. After leaving the...
  11. T

    A falling stone takes 0.28 s to travel past a window 2.2 m...

    Homework Statement A falling stone takes 0.28 s to travel past a window 2.2 m tall. From what height above the top of the window did the stone fall? So from this problem I think I have these variables: vo = ? (or 0 because falling usually indicates 0 for an initial velocity?) yo = 0 y = 2.2m...

    Classical mechanics : constant acceleration

    Homework Statement Two cyclists, Anant and Beth, are standing on a straight road a distance d=22.0 m apart. Simultaneously, they begin to move toward each other, Anant with acceleration a_A=0.2 m/s^2 and Beth with acceleration a_b=0.10 m/s^2. Just as they begin to move, a bee, sitting on...
  13. F

    MHB Interpreting Constant A & Deriving k in Air Pressure Decay

    hey guys! I'm really confused as to what this question is trying to ask me! can someone help me out :) Air pressure decays approximately exponentially at about 0.4 per cent for each rise of 30 metres above sea level. If we let p = p(h) denote air pressure (measured in some appropriate units) at...
  14. R

    Show the norm ||x|| is less or equal to A|x| for some constant A

    Homework Statement Show that \|x\| \leq A|x| \forall x \in \mathbb{R}, where A \geq 0. Homework Equations We know the norm is a function f: {\mathbb{R}}^{d} \to \mathbb{R}, such that: a) f(x) = 0 \iff x = 0, b) f(x+y) \leq f(x) + f(y), and c) f(cx) = |c|f(x) \forall c \in \mathbb{R}...
  15. R

    Is Planck's constant a paradox?

    The following is a quote from Wikipedia on Irrational Numbers (the bold is mine): If this is the case and there is no "small indivisible unit that could fit evenly into one of these lengths as well as the other", then how can Planck's Constant be true, unless it is a paradoxical number that is...
  16. A

    Finding Constant Acceleration of Train: Liz's Homework Solution

    Homework Statement Liz rushes down onto a subway platform to find her train already departing. She stops and watches the cars go by. Each car is 8.60 m long. The first moves past her in 1.50 s and the second in 1.10 s. Find the constant acceleration of the train. Homework Equations...
  17. N

    Limits: Find (in terms of the constant a)

    Homework Statement Find (in terms of the constant a) lim (√8(a+h) - √8a)/h h=>0 Homework Equations The Attempt at a Solution I tried a few ways of simplifying the numerator and trying to cancel out the h's but each time I try it doesn't come out right at all or I still...
  18. A

    Distance travel given constant a

    A hot rod can accelerate from 0 to 60 km/h in 5.4 s. (a) What is its average acceleration, in m/s2, during this time? (b) How far will it travel during the 5.4 s, assuming its acceleration is constant? (c) How much time would it require to go a distance of 0.32 km if its acceleration...
  19. F

    Motion that changes from constant a to constant v

    Homework Statement As soon as a traffic light turns green, a car speeds up from rest to 50 mi/h with constant acceleration 9.00mi/h*s. In the adjoining bike lane, a cyclist sppeds up from rest to 20 mi/h with constant acceleration 13mi/h*s. Each vechicle maintains constant velocity after...
  20. W

    Computing Normalisation Constant A

    Homework Statement Question: Given that Wavefunction Fi = A exp[b*mod(x)], which b is a non zero positive constant. Calculate the normalisation constant. Homework Equations 1 = Integrating Mod square (Wavefunction) from minus infinity to positive infinity The Attempt at a Solution...
  21. M

    Find Constant A in IV Diode Characteristic: Urgent Homework

    Homework Statement this is a lab task, i have found out the IV characteristic of the diode, now they ask me to suggest a procedure to find the constant A, in the equation I= AT^3 x exp (-E/ kT), T being the temperature, and I = saturation current Homework Equations i know how to...
  22. M

    Find Constant A in IV Diode Characteristic - Urgent Homework

    Homework Statement this is a lab task, i have found out the IV characteristic of the diode, now they ask me to suggest a procedure to find the constant A, in the equation I= AT^3 x exp (-E/ kT), T being the temperature, and I = saturation current Homework Equations i know how to...
  23. ~christina~

    When will Kathy overtake Stan if he starts 1.00s before her with constant a

    Homework Statement Kathy has a sports car that can accelerate at the rate of 4.90m/s^2. She races with Stan. Both cars start from rest but experienced Stan leaves starting line 1.00s before her. Stan moves with a constant aceleration of 3.90m/s^2 and Kathy maintains an acceleration of...
  24. DaveC426913

    Time as a function of distance for constant a

    I want to make a little calculator that will - take a distance (such as, say, 20.7 light years) and, - with a given acceleration (say, 1g) followed by deceleration, spit out the time elapsed. I don't know how to fold Lorentz' velocity function into the formula for t as a function of d...
  25. P

    Finding the Normalization Constant for a Wave Function with Given Parameters

    Homework Statement The wave function of a particle is Y(x,t) = A e^-kx*e^-iwt for x greater than or equal too 0, and it is zero everywhere else. What is the numerical value of the normalization constant A for k=5.55 1/nm and w =7.19 1/ps? Homework Equations intergral Y^2=1 The...