Question #9a262

2 Answers
Jan 28, 2015

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")

Jan 28, 2015

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