Question

The thermal capacity of 40 g of aluminium \[\left( {\text{specific heat }= 0.2\,cal/g{}^0C} \right)\] is?
A. \[40cal/{}^0C\]
B. \[160cal/{}^0C\]
C. \[200cal/{}^0C\]
D. \[8cal/{}^0C\]

Answer 1

Hint: The thermal capacity of a body is defined as the heat required to raise the temperature of the given body by one degree. On the other hand we can also express the heat capacity formula as the product of mass, specific heat, and change in temperature. Change in thermal energy can be calculated by the formula:Change in thermal energy = mass $\times$ specific heat capacity $\times$ change in temperature. Here the change in temperature is calculated by subtracting the initial temperature from the final temperature.

Formula used:
Specific heat capacity is given as:
\[Q = mc\Delta T\]
Where Q is the heat energy, m is the mass, c is the specific heat capacity and \[\Delta T\] is the change in temperature.

Complete step by step solution:
Given mass of aluminium, m= 40 g
\[\left( {\text{specific heat }= 0.2\,cal/g{}^0C} \right)\]
As we know that thermal capacity,
\[Q = m \times c \times \Delta t\]
Here we see that \[Q \propto c\].
Substituting the given values, we get
Thermal capacity, \[Q = 40 \times 0.2 \times 1\]
\[\therefore {\rm{ Q = 8\,cal/}}{}^0{\rm{C}}\]
Therefore, the thermal capacity of 40 g of aluminium \[\left( {\text{specific heat }= 0.2\,cal/g{}^0C} \right)\] is \[{\rm{8cal/}}{}^0{\rm{C}}\].

Hence option D is the correct answer

Note: Heat capacity is defined as the heat required to increase the temperature of an object by one degree. Heat gain as well as heat loss results in changes in temperature, state and performance of the work. Heat is also known to be a transfer of energy. The heat capacity is usually expressed in joules or in calories and temperature is expressed in Celsius or Kelvin. Any heat capacity problem can be calculating the heat capacity, mass or temperature difference of any given substance.