# If the change in temperature of the water is bigger, does it mean that more heat is l

1. Jan 6, 2010

### acronym

1. The problem statement, all variables and given/known data

If the specific heat capacity of water from an experiment is smaller than its actual value, does it mean more heat is lost to the surroundings? If the heat is emitted by a wire into a cup of water and the change in temperature is measured, does it mean that the change in temperature of the water would bigger if more heat is lost to the surroundings?

2. Relevant equations
∆T/time = (1/mc)*IV

3. The attempt at a solution
so if c is smaller (more heat energy lost to surroundings) then the RHS will be bigger, meaning the LHS must be bigger to balance the equation. Therefore ∆T must increase.

2. Jan 6, 2010

### acronym

Re: If the change in temperature of the water is bigger, does it mean that more heat

anyone???

3. Jan 7, 2010

### acronym

Re: If the change in temperature of the water is bigger, does it mean that more heat

no one :(

4. Jan 7, 2010

### mgb_phys

Re: If the change in temperature of the water is bigger, does it mean that more heat

Lower specific heat capacity means that less energy is lost to reduce temperature by the same amount.

I think you have a couple of questions/different principles confused here.
The rate of heat loss into the surroundings depends on the temperature difference.
How quickly this changes the temperature depends on the heat capacity.
It will also depend on the amount of power being supplie dby the wire.

What exactly is the question?

ps. replying to your own question if nobody answers is a bad idea - it marks the question as 'answered' so people ignore it. Remember PF readers are all over the world so it may take 12hours if you post it while the US or Europe is asleep.

5. Jan 7, 2010

### acronym

Re: If the change in temperature of the water is bigger, does it mean that more heat

In an ideal world, rate of thermal energy absorbed by the water = rate of electrical energy developed by the wire, as the wire gives off heat. But in the real world, some of the electrical energy converted into heat will not all go to heat up the water, but to the surrounding air instead, especially if the cup of water is not insulated. This will make the calculations for the SHC lower than the actual value.

It seems logical that since less heat is gone to heat up the water, the change in water temperature should be lesss--so c is smaller because ∆T is smaller.
However, in the formula ∆T/time = (1/mc)*IV it seems that if c smaller, ∆T will actually be larger (to balance the equation). So where is my reasoning going wrong?

Sorry, I seldom come to this site so I don't know how it works =/ Hope you'll answer my question...

6. Jan 7, 2010

### mgb_phys

Re: If the change in temperature of the water is bigger, does it mean that more heat

Ok - you are asking how will heat loss effect you measurement of SHC in the experiment?

If you supply a certain amount of electrical energy, and you assume that Q = mcT (with no heat lost).
Then if heat is lost to the surroundings you will measure that more energy is required to heat the water than is really true so you will determine that C is higher (it is harder to heat water) than is correct

7. Jan 7, 2010

8. Jan 7, 2010

### mgb_phys

Re: If the change in temperature of the water is bigger, does it mean that more heat

You would measure C as bigger than it is, so the value of C would be smaller than you measure.
The only equation is that Q is proportional to C

9. Jan 7, 2010

### acronym

Re: If the change in temperature of the water is bigger, does it mean that more heat

Oh...so it's hypothetical...
we imagine that Q will have to increase because more energy will be needed for the water to reach the same temperature without heat loss...so c must also be considered bigger to balance the equation.

Therefore in reality, c should be smaller since Q absorbed is less (due to heat loss)?

10. Jan 16, 2010

### acronym

Re: If the change in temperature of the water is bigger, does it mean that more heat

well, thanks a bunch!^^