Meaning of symbols in given equation

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Discussion Overview

The discussion revolves around the meaning of the symbol 'J' in the equation W=JQ, which relates work done (W) to heat supplied (Q) in the context of the First Law of Thermodynamics. Participants explore the implications of using different units for heat and work, as well as the historical context of these measurements.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant seeks clarification on what 'J' represents in the equation W=JQ, noting that the textbook does not define it.
  • Another participant identifies 'J' as the mechanical equivalent of heat, explaining its role as a conversion constant between calories and joules.
  • Some participants discuss the historical context of measurement units, mentioning that older textbooks may use different units such as British Thermal Units and horsepower.
  • A participant questions the dimensional consistency of 'J', suggesting that it appears to be a constant without units in the equation.
  • Another participant suggests that examining other problems in the textbook may help clarify the system of units being used.
  • One participant expresses satisfaction with the explanation provided, indicating that the clarification helped them understand the equation better.

Areas of Agreement / Disagreement

There is no consensus on the interpretation of 'J' as some participants agree on its meaning while others raise questions about its dimensionality and the context of the equation. The discussion remains unresolved regarding the implications of using different units.

Contextual Notes

Participants note that the equation is presented as a basic formula without context for its application, leading to uncertainty about the units and dimensions of 'J'.

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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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
 

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