Meaning of symbols in given equation

  • Thread starter Thread starter HUMERA.S
  • Start date Start date
  • Tags Tags
    Symbols
AI Thread Summary
In the equation W = JQ from the First Law of Thermodynamics, 'J' represents the mechanical equivalent of heat, specifically the conversion factor of 4.18 joules per calorie. This equation illustrates the relationship between work done (W) and heat supplied (Q), both of which are forms of energy. Historically, different units like calories and joules were used for heat and work, but modern practice favors using joules for consistency. The discussion clarifies that 'J' serves as a conversion constant, ensuring both quantities are measured in compatible units. Understanding this relationship simplifies the application of the equation in thermodynamic problems.
HUMERA.S
Messages
9
Reaction score
0
In my textbook, under the subtopic 1st law of of Thermodynamics, an equation is given as foll :
W=JQ
where W=work done ;Q=heat supplied
but they have not mentioned what is J.

please could someone tell me what exactly 'J' stands for in this equation
 
Physics news on Phys.org
Is this an old textbook?

J is the symbol for a quantity called 'The mechanical equivalent of heat'.

Both heat and work are forms of energy (as are all the other terms in the First Law) but we need to ensure that they are all in the same units.

At one time, the metric measure for heat was the calorie, whilst the unit for work was the joule. Today we measure it all in joules.

J is simply the conversion constant and is equal to 4.18 joules per calorie.
 
Studiot said:
At one time, the metric measure for heat was the calorie, whilst the unit for work was the joule. Today we measure it all in joules.

And if it was an old American textbook, it might be using Brithsh Thermal Units and horsepower...

It's mich simpler to use SI units, and measure both heat and work in the same units (joules).
 
well yeah I know in S.I. 'J' stands for joule...

but in the equation W=JQ ; if we consider W(work) and Q(energy) in the same units, then here J seems to be some constant with no units and no dimensions ! [as 'J' relates W & Q with a multiplication and not addition or substaction]

the equation was not given while solving a problem , but was stated like it is a basic formula.
 
HUMERA.S said:
but in the equation W=JQ ; if we consider W(work) and Q(energy) in the same units, then here J seems to be some constant with no units and no dimensions ! [as 'J' relates W & Q with a multiplication and not addition or substaction]

the equation was not given while solving a problem , but was stated like it is a basic formula.
By looking through other worked problems in that textbook you should be able to deduce the system of units that book uses.

I believe Studiot provided you with a very good explanation:

Work (in joules) = (4.18 joules per calorie) x Q (in calories)

illustrating how J has a value and units
 
"Work (in joules) = (4.18 joules per calorie) x Q (in calories)"

Wow really its clear now !
Thanks a lot
 
Thread 'Gauss' law seems to imply instantaneous electric field propagation'

Thread 'Gauss' law seems to imply instantaneous electric field propagation'

Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
View full post »

Thread 'Do electron density waves accompany EM waves in coaxial cables?'

Maxwell’s equations imply the following wave equation for the electric field $$\nabla^2\mathbf{E}-\frac{1}{c^2}\frac{\partial^2\mathbf{E}}{\partial t^2} = \frac{1}{\varepsilon_0}\nabla\rho+\mu_0\frac{\partial\mathbf J}{\partial t}.\tag{1}$$ I wonder if eqn.##(1)## can be split into the following transverse part $$\nabla^2\mathbf{E}_T-\frac{1}{c^2}\frac{\partial^2\mathbf{E}_T}{\partial t^2} = \mu_0\frac{\partial\mathbf{J}_T}{\partial t}\tag{2}$$ and longitudinal part...
View full post »
Thread 'Recovering Hamilton's Equations from Poisson brackets'

Thread 'Recovering Hamilton's Equations from Poisson brackets'

The issue : Let me start by copying and pasting the relevant passage from the text, thanks to modern day methods of computing. The trouble is, in equation (4.79), it completely ignores the partial derivative of ##q_i## with respect to time, i.e. it puts ##\partial q_i/\partial t=0##. But ##q_i## is a dynamical variable of ##t##, or ##q_i(t)##. In the derivation of Hamilton's equations from the Hamiltonian, viz. ##H = p_i \dot q_i-L##, nowhere did we assume that ##\partial q_i/\partial...
View full post »

Similar threads

A Meaning of "symbol" in algebraic field theory?
Replies
5
Views
1K
I How Does Temperature Affect Wire Tension at Constant Length?
Replies
4
Views
2K
I How to measure average thermal conductivity of a metallic material?
Replies
1
Views
2K
B Struggle to understand adiabatic process
Replies
2
Views
1K
Work greater than heat given to colder reservoir -- impossible?
Replies
18
Views
1K
First law of thermodynamics and the work done on a system
Replies
13
Views
2K
Chemistry Show that book levitation by absorption of heat violates 2nd law
Replies
13
Views
2K
A Question on Drift-Diffusion Equation
Replies
6
Views
2K
Chemistry How to derive 2nd law extremum principles for U, A, G, and H?
Replies
1
Views
2K
I Why is first TD law different for chemical reactors
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top