Question

The heat capacity for aluminum is $0.89{\text{ J}}{{\text{g}}^{{\text{ - 10}}}}{{\text{C}}^{{\text{ - 1}}}}$, for iron is $0.45{\text{ J}}{{\text{g}}^{{\text{ - 10}}}}{{\text{C}}^{{\text{ - 1}}}}$, and for zinc is $0.39{\text{ J}}{{\text{g}}^{{\text{ - 10}}}}{{\text{C}}^{{\text{ - 1}}}}$. If $100$J of heat energy was added to a $10$g sample of each of the metals, which of the following would be true?
A) Al would have the largest temperature increase.
B) Fe will have the largest temperature increase.
C) Zn would have the largest temperature increase.
 D) Fe and Zn would have the same increase.
E) All three metals would have the same temperature increase.

Answer 1

Hint:We will use the formula of heat capacity which gives the relation between change in temperature, mass, and amount of heat required and is given as-
$ \Rightarrow {\text{s = }}\dfrac{{\text{Q}}}{{{{m\Delta T}}}}$
Where s is specific heat capacity, m is the mass of the sample, Q is the amount of heat added and ∆T is the change in temperature. Put the given values in the formula and calculate temperature change for zinc, aluminum, and iron. The element having a large change in temperature will have the largest temperature increase.

Complete step-by-step answer:Given, heat capacity of aluminum=$0.89{\text{ J}}{{\text{g}}^{{\text{ - 10}}}}{{\text{C}}^{{\text{ - 1}}}}$
And heat capacity of iron=$0.45{\text{ J}}{{\text{g}}^{{\text{ - 10}}}}{{\text{C}}^{{\text{ - 1}}}}$
And heat capacity of zinc=$0.39{\text{ J}}{{\text{g}}^{{\text{ - 10}}}}{{\text{C}}^{{\text{ - 1}}}}$
Now, since $100$J energy is added so Q=$100$J
And the given mass of sample of each metal (m) =$10$g.
We know that heat capacity is expressed by the formula –
$ \Rightarrow {\text{s = }}\dfrac{{\text{Q}}}{{{{m\Delta T}}}}$
Where s is specific heat capacity, m is the mass of the sample, Q is the amount of heat added and ∆T is the change in temperature.
 On putting all the given values in this formula we get,
-For Zinc,
$ \Rightarrow 0.39 = \dfrac{{100}}{{10 \times \Delta T}} \\
 \Rightarrow \Delta T = \dfrac{{100}}{{10 \times 0.39}} = 25.64 \\ $
For Aluminum,
$ \Rightarrow 0.89 = \dfrac{{100}}{{10 \times \Delta T}} \\
 \Rightarrow \Delta T = \dfrac{{100}}{{10 \times 0.89}} = 11.23 \\
$
For Iron,
$
\Rightarrow 0.45 = \dfrac{{100}}{{10 \times \Delta T}} \\
 \Rightarrow \Delta T = \dfrac{{100}}{{10 \times 0.45}} = 22.22 \\ $
Now, we will compare the temperature change for zinc, aluminum, and iron.
On comparing, we get-
$ \Rightarrow 25.64 > 22.22 > 11.23$
 Since the temperature change in Zinc is highest, So Zn has the largest temperature increase.

Hence the correct answer is ‘C’.

Note:In this question, to calculate the largest temperature increase we are calculating the change in temperature as the large temperature change will indicate a large temperature increase. Heat capacity is already given so we use the formula of heat capacity to calculate it. If in this type of question, we are asked to find the least temperature increase, then also we will solve using the same method.