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The specific heat of wood is \[2.03J{{g}^{-1}}{}^\circ C\]. How much heat is needed to raise the temperature of $550g$ of wood from $-15{}^\circ C$ to $10{}^\circ C$?

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Last updated date: 13th Jun 2024
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Answer
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Hint: The specific heat of any substance is the heat required by one gram of that substance in order to raise the temperature of that substance by one unit.
The formula to calculate the heat of a system establishes a relationship between the change in temperature of the system and the specific heat of the system.

Complete solution:
In order to solve this question we will need a formula or an equation, which connects the specific heat of a substance with the temperature. So we will be using the formula,
\[q=m\times c\times \Delta T\]
Where, $q$ is the amount of heat given to the system, $m$ represents the mass of the sample, $c$ signifies the specific heat of the wood under consideration and $\Delta T$ is the change observed in temperature, which is the difference in temperature of initial and final value.
Specific heat of a substance can be defined as the amount of heat required by one gram of the substance in order to raise the temperature by one unit. Now if we consider the value given in the question, we need $2.03J$ of heat in order to raise the temperature of one gram wood by one degree Celsius. Now we will calculate the amount of heat required to raise the temperature of $550g$ of wood. So, we will substitute the values on the above equation, and we get,
$q=550g\times 2.03\dfrac{J}{g{}^\circ C}[10-(-15)]{}^\circ C$
Now, we will solve this equation, and we get, $27912.5J$. As we know that it is necessary to express the quantities in significant figures, and also we will express it in the units of kilojoule.
So we get, $q=28kJ$ which is the required answer.

Note: The quantity of heat should be preferably expressed in kilojoules, rather than joules when the value is high. The heat of a substance can be calculated by using the value of specific heat and the change in temperature along with the amount of substance, by using a direct formula which relates all these quantities together.