# How much energy in Joules is released as 100 g of aluminium (specific heat 0.900 J / g degrees...

## Question:

How much energy in Joules is released as {eq}100\ g {/eq} of aluminium (specific heat {eq}\rm 0.900\ J / g ^\circ {/eq} Celsius) cools from {eq}100.0 ^\circ {/eq} Celsius to {eq}30.0 ^\circ {/eq} Celsius?

## Heat Transfer Equation:

The heat transferred is proportional to the change in the temperature of a substance. During this heat transfer, we must also consider the mass and the specific heat of the substance. We can determine the total heat transferred to the substance through the equation, {eq}\displaystyle q = mc\Delta T {/eq}, where {eq}\displaystyle m {/eq} is the mass, {eq}\displaystyle c {/eq} is the specific heat and {eq}\displaystyle \Delta T {/eq} is the change in temperature.

Determine the energy released by the aluminum, {eq}\displaystyle q {/eq}, that a sample with a mass of {eq}\displaystyle m= 100\ g {/eq} cooled down at a change of {eq}\displaystyle \Delta T = 30 ^\circ C-100 ^\circ C= -70 ^\circ C {/eq}, using the equation, {eq}\displaystyle q = mc\Delta T {/eq}, where {eq}\displaystyle c = 0.900\ \rm{J/g ^\circ C} {/eq}. We proceed with the solution.

{eq}\begin{align} \displaystyle q &= mc\Delta T\\ &= 100\ g\times 0.900\ \rm{J/g ^\circ C}\times -70 ^\circ C\\ &=-6300\ J \end{align} {/eq}