Question

A sample of mercury absorbed $257J$ of heat and its mass was $0.45kg$ . If it’s temperature increased by $4.09K$ , what is its specific heat in $J{\left( {kg.K} \right)^{ - 1}}$ ?

Answer 1

When a certain amount of heat energy is given to the sample, then the temperature will change. Given that a sample of mercury is absorbed $257J$ , the temperature difference and mass were given. By substituting these values in the below formula, the specific heat can be determined.
$c = \dfrac{Q}{{m.\Delta T}}$
$c$ is specific heat
$Q$ is amount of heat absorbed by a mercury sample
$m$ is mass of mercury sample
$\Delta T$ is a change or difference in temperature.

Complete Step By Step Answer:
Specific heat is the amount of heat required to raise the temperature of a unit mass of substance through one degree centigrade. It was generally represented by $c$ .
Mercury is the only non-metal that can exist as liquid in the periodic table. When a certain amount of energy is given to the mercury sample, it results in the absorption of that energy.
The amount of heat absorbed is $257J$
The mass of mercury sample is $0.45kg$
The change in temperature is $4.09K$
Substitute the values in the above formula,
$c = \dfrac{{257J}}{{\left( {0.45kg} \right) \times \left( {4.09K} \right)}} = 140J{\left( {kg.K} \right)^{ - 1}}$
Thus, when a sample of mercury absorbed $257J$ of heat and its mass was $0.45kg$ . If it’s temperature increases by $4.09K$ then the specific heat is $140J{\left( {kg.K} \right)^{ - 1}}$ .

Note:
In the given problem, energy is given in joules, and temperature is in kelvins, mass is in kilograms. If any one of the terms has different units, then it should be converted into these units only. As the desired specific heat value should be in $J{\left( {kg.K} \right)^{ - 1}}$ .