Question

Question #9a262

Answer 1

The symbol `"q"` is used to express either heat absorbed or heat lost, although heat lost is usually written as `"-q"`.

As you know, the formula for calculating heat gained is

`"q" = m * c * DeltaT"`, where

`m` - the mass of the substance;
`c` - its specific heat;
`DeltaT` - the difference between the final and the initial temperature of the substance.

In your case, you have a metal that is probably heated and then placed in water. The water would heat up by a number of degrees, while the metal would cool down by a much greater number of degrees. The heat lost by the metal will be equal to

`"-q" = m_("metal") * c_("metal") * DeltaT_("metal")`

This will get you

`c_("metal") = ("-q")/("m"_("metal") * DeltaT_("metal")`

Since the metal is cooling off, its final temperature will be lower than its initial one, so `DeltaT_("metal")` will be negative `->` the negative signs will cancel out.

As a conclusion, `"q"` represents either the heat lost by the hot metal, or the heat gained by the water, since what is lost by the metal must be gained by the water.

`-q_("metal") = q_("water")`

Answer 2

The equation for heat and temperature change is:

`Q=c*m*DeltaT`

Where `Q` = total warmth energy (in `J` for Joules)
`c` = specific heat capacity (in `J//g*K`)
`m` = mass (in `g` for grams)
`DeltaT` = temperature difference (after-before) (in `K` or `C`)

If `m` (mass) is twice as high, you will need twice `Q` for the same effect. Same goes for a greater `DeltaT` temperature difference.

If you want to determine `c` the equation becomes:

`c=Q/(m*DeltaT`

And it then depends how you supplied the heat. If you do this electrically (by a heating element) the other half of the equation becomes:

`E=U*I*t`

Where `E` = energie provided (also in `J`)
`U` = voltage (in `V`)
`I` = current (in `A`)
`t` = time (in `s` seconds)

Assuming there are no losses (but there always are), you can set `E` equal to `Q` to get:

`c=(U*I*t)/(m*DeltaT`