# Question 9a262

Jan 28, 2015

The symbol $\text{q}$ is used to express either heat absorbed or heat lost, although heat lost is usually written as $\text{-q}$.

As you know, the formula for calculating heat gained is

$\text{q" = m * c * DeltaT}$, where

$m$ - the mass of the substance;
$c$ - its specific heat;
$\Delta T$ - 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

${c}_{\text{metal") = ("-q")/("m"_("metal") * DeltaT_("metal}}$

Since the metal is cooling off, its final temperature will be lower than its initial one, so $\Delta {T}_{\text{metal}}$ will be negative $\to$ the negative signs will cancel out.

As a conclusion, $\text{q}$ 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.

$- {q}_{\text{metal") = q_("water}}$

Jan 28, 2015

The equation for heat and temperature change is:

$Q = c \cdot m \cdot \Delta T$

Where $Q$ = total warmth energy (in $J$ for Joules)
$c$ = specific heat capacity (in $J / g \cdot K$)
$m$ = mass (in $g$ for grams)
$\Delta T$ = 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 $\Delta T$ 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:

$E = U \cdot I \cdot t$

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#