I need an equation to calculate joules of heat from joul

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bradlee

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Please help, I need an equation to calculate, in joules, the amount of heat that is created by an electrical test circuit inside a calorimeter.

Note: the circuit's input power supply is a capacitor charged to a certain voltage and discharges with nonlinear voltage and current.Although total joules of input power have been calculated, I suspect this may make future calculations difficult.

Also,a "power under the curve" has been drawn on graph paper showing temperature over time.
The big question is when I count up the squares
how do I convert this data into joules and then use this to calculate the efficiency of the test circuit. Any and all help is welcomed. Thanks Brad
 
Re: I need an equation to calculate joules of heat from joul

Originally posted by jwelectric:
1 BTU = 1050 joules
1 calorie = 4.186 joules
1 watt = 1 joule
Click to expand...
Nuh-uh!

1 joule = 1 watt-second

Power is power and energy is energy
 
Re: I need an equation to calculate joules of heat from joul

The question is not about converting one unit of energy to another unit of energy. The question is how to calculate the output energy, given only the observed change in temperature over time.

The answer is "you can't." More precisely, "you can't calculate the output energy from the information that was given."

If your plot is really showing temperature as a function of time, then the "squares" that you are adding up have no physical significance. When you add the squares under a curve, you are essentially performing a mathematical "integration." Whatever numerical answer you come up with, the unit of measure that is associated with that number will be the unit of measure of the vertical axis times the unit of measure of the horizontal axis. For your case, you are adding up squares that will tell you the number of "degree-seconds" that are under the curve.

Whatever "degree-seconds" might be, as a unit of measure, it is not a unit of energy. You cannot convert "degree-seconds" to "joules."

What is missing here is the relationship between the temperature rise of the element that is being heated and the energy it takes to obtain that temperature rise. You need to know the nature of the element.
 
Re: I need an equation to calculate joules of heat from joul

Thanks Charlieb for pointing me in the right direction. Question--If i had the values of the element could i then be able to calculate joules from the "power under curve"? If so How?
Almost forgot the element is an array of small low voltage light bulbs-the problem is as they heat and cool the resistance changes- from this how can I come up with a value to use for other calculations. Thanks for your time and help Brad
 
Re: I need an equation to calculate joules of heat from joul

Charlie
A big Duh goes to me for having "power under the curve" on the brain. What i should have said was once I had the values of the element could I use the temperature and time charted in my calculations--SORRY
 
Re: I need an equation to calculate joules of heat from joul

A plot of temperature versus time is not going to tell you anything by itself. What you need is a plot of power versus time. The integral of that curve will be energy.

But what is still missing is the correlation of the temperature of the element to the power being consumed by the element. The discipline of Electrical Science is not going to give you that information. This is a matter of Materials Engineering, and is not far from the borders of Thermodynamics. I tend to shudder, when I get anywhere near that border.

Knowing the resistance of the filaments in each light bulb will not help. Sure, you can calculate the power in a resistive element (i.e., light bulb filament) by knowing its resistance and the applied voltage. But as you pointed out, the resistance is not a constant. So the formula P = I^2R (or V^2/R) will not help.

You need to use the integral form, P = the integral of I(t)^2 times R(t) times dt.

If you want to use this by "counting squares" on graph paper, instead of performing a numerical integration, then you need to get a plot of current (as a function of time) and a plot of resistance (as a function of time). Then, point by point, you square the current curve, multiply it by the resistance curve, plot that against time, and you can get your energy value.

But from what you have told us so far, your experiment did not measure current or resistance. You measured temperature. Current you should be able to measure directly. It may be possible to obtain a correlation between temperature and resistance. That is in the realm of Materials Engineering, as I said before. I can't take you any further down that road, as I did not like, or do well in, my Materials classes.

Another complicating factor is the difference between the temperature at the point at which you took your measurements and the actual temperature of the filaments themselves. The filaments are inside the bulb and are some distance from the glass. I don't know how close your temperature sensor was to the bulb, but any air between the bulb's glass and the sensor will further distort your temperature measurements.
 
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