Question

The temperature of a bar rises by $10{}^ \circ C$ when it absorbs $1.23\;kJ$ of energy by heat. The mass of the bar is $525\;g$. Determine the specific heat of silver

Answer 1

The formula for the specific heat of a material is applied and the given values of data from the above question must be substituted to obtain the value of specific heat of silver. The formula relates the energy absorbed in joules, the mass of the bar and the temperature difference and the specific heat of a given material is given by the amount of heat absorbed divided by its mass and the change in temperature.

Formula used: The formula relating this absorption of heat of a material with its mass, change in temperature and the specific heat is as follows:
$Q = mc\Delta T$
Where, $Q$ is the heat transfer in joules, $m$ is the mass, $c$ is the specific heat of the material and $\Delta T$ is the change in temperature.

Complete step by step answer:
The bar of silver absorbs heat energy and hence the temperature rises by an amount of $10{}^ \circ C$. This rise in temperature is due to the property of heat transfer between two bodies through the process of conduction (in this case) as silver is a conductor of heat.The specific heat of a material specifies the amount of heat energy required to raise the temperature of a substance per unit of mass. It is the heat required to raise the temperature of a $1\;g$ sample by a temperature of $1\;K$ or $1{}^ \circ C$.

As per the formula for heat absorption we know that,
$Q = mc\Delta T$
The terms are rearranged in-order to make $c$ the subject since we are required to find the value of specific heat. We get:
$\Rightarrow c = \dfrac{Q}{{m\Delta T}}$ ----($1$)
The data that is given in the question is as follows:
$Q = 1.23\;kJ$
$\Rightarrow m = 525\;g$
$\Rightarrow \Delta T = 10{}^ \circ C$
Since the SI unit of heat transfer is in joules we do the required conversion:
$1\;KJ = 1000\;J$
$\Rightarrow Q = 1.23 \times {10^3}\;J$

The SI unit of mass is always kilograms and hence we do the required conversion:
$1\;g = \dfrac{1}{{1000}}\;kg$
$\Rightarrow m = 525\;g = 0.525\;kg$
Next, we substitute all the given values in the equation ($1$). The specific heat of silver is given by:
$\Rightarrow {c_{silver}} = \dfrac{{1.23 \times {{10}^3}}}{{0.525 \times 10}}$
$\Rightarrow {c_{silver}} = 234.285\;Jk{g^{ - 1}}{C^{ - 1}}$
This is approximated and rounded off to $3$ significant figures.
$\therefore {c_{silver}} \approx 234\;Jk{g^{ - 1}}{C^{ - 1}}$

Hence the specific heat of silver determined is $234\;Jk{g^{ - 1}}{C^{ - 1}}$.

Additional information: Any material (can be liquid or solid) which absorbs heat energy depends on its mass, the change in temperature and the nature of the substance.There is a change in temperature that is observed. However, this change may vary from substance to substance and hence every substance consists of a unique value for the amount of heat absorbed or released by a unit mass. The property of specific heat capacity signifies the change in temperature of the substance when a given quantity of heat is absorbed or released by it; given that there is no change in phase.

Note: It is necessary to take into consideration that the temperature quantity is undergoing a change and hence this difference must be taken and not a single static value of temperature which is a common misconception. We must also see whether the heat is being absorbed or released by the material.