Meaning of symbols in given equation

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In summary, J in the equation W=JQ stands for the mechanical equivalent of heat, which is a conversion constant used to ensure that both heat and work are measured in the same units. It is equal to 4.18 joules per calorie and is commonly used in textbooks as a basic formula. Its value and units can be deduced by looking through other worked problems in the same textbook.
  • #1
HUMERA.S
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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
 
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  • #2
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.
 
  • #3
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).
 
  • #4
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.
 
  • #5
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
 
  • #6
"Work (in joules) = (4.18 joules per calorie) x Q (in calories)"

Wow really its clear now !
Thanks a lot
 

1. What is the significance of symbols in an equation?

The symbols in an equation represent different mathematical quantities or operations. They help to convey the relationship between the different variables and constants in the equation.

2. How do I interpret the meaning of symbols in an equation?

The meaning of symbols in an equation can be interpreted by understanding their mathematical definitions and how they are used in the context of the equation. It is important to consider the units of each symbol and their role in the overall equation.

3. Can symbols in an equation have multiple meanings?

Yes, symbols in an equation may have multiple meanings depending on the context in which they are used. It is important to consider the specific equation and its purpose when determining the meaning of symbols.

4. Why are symbols used in equations instead of words?

Symbols are used in equations because they are concise and universally understood by mathematicians and scientists. They also allow for complex mathematical concepts to be represented more efficiently and clearly.

5. How do I know which symbols to use in a specific equation?

The symbols used in an equation are typically defined within the context of the equation or in a key/legend. It is important to carefully read and understand the equation before determining which symbols to use. Also, it is helpful to be familiar with commonly used symbols in mathematics and science.

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