Question

How much heat does it take to raise the temperature of 2.5 kg of plastic from $15{}^\circ C$ to $75{}^\circ C$?
The specific heat of plastic is 2.60 $kJ/(kg.{}^\circ C)$.

Answer 1

Hint:The amount of heat that is required by a substance to produce a unit change in its temperature is known as the heat capacity of a substance or thermal capacity. Its SI unit is joules per kelvin or J/K.
We get the specific heat capacity of a substance when we divide the heat capacity of the substance by its mass. Its SI unit is joules per kelvin and kilogram or J/kg.K.

Complete step-by-step answer:We know that to change the temperature of one unit of mass of a substance by one degree, the amount of energy that is required is equivalent to the specific heat capacity of the substance.
Now, from the definition, we can see that specific heat capacity is
\[c=\dfrac{C}{m}=\dfrac{Q}{\Delta T\times m}\]
Where c is the specific heat capacity, C is the heat capacity (J/K) of the substance, Q is the heat energy (joules), m is the mass of the substance (kg), and $\Delta T$is the change in the temperature (K).
Now, the relation between the heat energy required to change the temperature of a substance and the specific heat capacity of a substance is given by
\[Q=mc\Delta T\]
In the given question, it is known that
m = 2.5 kg,
c = 2.60 $kJ/(kg.{}^\circ C)$,
and $\Delta T=75{}^\circ C-15{}^\circ C=60{}^\circ C$.
By substituting these values in the heat energy formula, we get
\[Q=2.5kg\times 2.6kJ/(kg.{}^\circ C)\times 60{}^\circ C \\
Q=390kJ \\
\]
Hence 390kJ of heat energy is required to raise the temperature of 2.5 kg of plastic from $15{}^\circ C$ to $75{}^\circ C$.

Note: It should be noted that the specific heat capacity of a substance is different for different states of matter. It also depends on the starting temperature of the substance and the pressure applied to the substance.