Question

How many joules of heat are needed to raise the temperature of 10.0 g of aluminum from $22{}^\circ C$ to $55{}^\circ C$, if the specific heat of aluminum is $0.90 J/g{}^\circ C$?

Answer 1

Hint: The specific heat of any substance or compound is the heat required by one gram of that compound to raise its temperature by one degree Celsius.

Formula used: Heat energy formula: $q= mc \Delta $T

Complete answer:
We have been given the data that, specific heat of aluminum is $0.90 J/g{}^\circ C$, and we have 10.0 g of aluminum, we are asked about the heat required in joules to raise the temperature of this amount of aluminum from $22{}^\circ C$ to $55{}^\circ C$.
As specific heat of aluminum is $0.90 J/g {}^\circ C$, this will be the heat required by aluminum to raise the temperature of 1 gram of aluminum by 1 degree Celsius. We are given 10.0 g of aluminum, so ten times the specific heat of aluminum will be required.
Now the temperature needs to be raised from $22{}^\circ C$ to $55{}^\circ C$. Which means the value of change in temperature, $\Delta $T will be:
$\Delta T= 55{}^\circ C- 22{}^\circ C$
$\Delta T= 30{}^\circ C$
Now, using the formula $q= mc \Delta $T where, q is the heat to be found, m is the mass of aluminum, c is the specific heat of aluminum, and $\Delta T$ is the change in temperature. We will calculate the heat as:
$q= mc\Delta T$
$q = 10.0 g \times 0.90 J/g {}^\circ C\,\times \,33{}^\circ C$
$q = 297 J$
Hence, the heat required by 10.0 g of aluminum to raise the temperature from $22{}^\circ C$ to $55{}^\circ C$ is 297 Joules.

Note:
The change in temperature,$\Delta $T , is the difference in the final temperature and the initial temperature, so do not take the difference as initial subtracting final temperature.