Why is heating coil data logarithmic instead of linear in IV vs ΔT?

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clarissalehne
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Specific Heat Capacity Lab

I conducted a lab where I heated 100ml of water using a heating coil with a current of 4A passing through it. The temperature data turned out beautifully, with the temperature rising evenly until it plateaued just under 100 degrees celsius as it began to change phase.

My aim was to find the specific heat capacity of the water by graphing IV (current times voltage) against ΔT (change in temperature) as this would give me a slope equal to mc/t.

Theory:
P=VI
P/t=Q
Q=tVI
Q=mcΔT

--> tVI=mcΔT

Strangely though, the graph of IV vs. ΔT is not linear but follows a logarithmic regression. When I plot IV vs. LN(ΔT) I get a linear graph. How can I find a slope that I can use to find the specific heat capacity? Also, is there something wrong with my data? Should the relationship be linear?
 
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Even though I don't know how you did what you did, I will try to help you. What kind of time is t in your expression? The time required for what to happen?
 
t was my independent variable. I monitored how the temperature of the water increased over time t. Does that make sense?
 
So t = 0 is when you started heating and t is some later time when the temperature of the water reached value T. Is that so?
 
T is the dependent. I think I have about a hundred values for each. T keeps increasing until it reaches the boiling of water.
 
clarissalehne said:
T is the dependent. I think I have about a hundred values for each. T keeps increasing until it reaches the boiling of water.
Please answer my questions

1. Is t the overall time from when the experiment started to when the water reached some intermediate temperature between the initial and the boiling point?

2. Is T the temperature at time t as defined above?

A simple "yes" or "no" to each of the two questions above is sufficient at this point. As I said, I am trying to understand what you did and what your symbols mean.