Question

How much energy must be transferred to raise the temperature of a cup of coffee $(250mL)$ from ${20.5^\circ }C\;(293.7K)$ to ${95.6^\circ }C\;(368.8K)$? Assume that water and coffee have the same density $(1.00gm{L^{ - 1}})$, and specific heat capacity $4.184J\;g{K^{ - 1}}$?

Answer 1

As we know that the specific heat of a substance is that amount of heat which is required to raise the temperature of unit mass of a substance usually by one degree and it is determined by the ratio of energy to the mass of that substance and the change in temperature.

Complete step-by-step answer:
As we have already discussed that the specific heat is expressed in terms of the heat energy supplied to the substance to raise the temperature, mass of that substance and change in temperature and it is normally expressed as shown below:
$\Rightarrow C = \dfrac{Q}{{m \times \Delta T}}$
Where, $\Delta T$ is the change in temperature and is determined by the difference of lower and higher temperature, $Q$ is the energy required to raise the temperature.

Now, we are given with the volume of the coffee cup which is $250mL$ and the density is $1.00gm{L^{ - 1}}$ so we can calculate the mass of the coffee cup because density is given as the ratio of mass and volume as:
$\Rightarrow density = \dfrac{{mass}}{{volume}}$
$\Rightarrow mass = density \times volume$
$\Rightarrow mass = 250 \times 1.00 = 250g$

Now, we also have specific heat capacity which is $4.184J\;g{K^{ - 1}}$ the heat required to raise the temperature would be given as:
$\Rightarrow Q = 250 \times 4.184 \times (368.8 - 293.7)$
$\Rightarrow Q = 77500J = 77.5kJ$

Therefore, from the above calculation we can say that the correct answer is $77.5kJ$ amount of heat energy is required to raise the temperature of the coffee cup.

Additional information: The heat capacity or heat energy is defined as the physical property of a matter which is used as to supply to a given mass of a substance so as to produce a change in temperature by exactly a unit.

Note: Always remember that the specific heat of a substance is a tool which determines the heat capacity of a heated as well as a cooled sample. We use the specific heat to basically raise the temperature of a substance usually by one degree.