Question

The thermal capacity of \[40g\] of aluminium \[(s = 0.2cal/gK)\] is
(A) \[168J/K\]
(B) \[672J/K\]
(C) \[840J/K\]
(D) \[33.6J/K\]

Answer 1

Hint: Specific heat is the amount of energy required to raise the temperature per unit mass of a substance. The units will be Calories per Kelvin or Joules per Kelvin. Whereas, thermal capacity is the amount of energy required to raise the temperature. The units will be calories per Kelvin.

Complete Step by Step Solution:
Aluminium is a chemical element with an atomic number \[13\] and placed in a group\[IIIA\]. Some of the chemical elements will absorb heat energy and undergo differences in temperature. The amount of energy given to raise the temperature per unit mass of a substance is nothing but the specific heat capacity of that element. It is denoted by \[S\].
Given that specific heat capacity, \[S = 0.2cal/gK\]. It has the units of calories per gram kelvin.

Thermal capacity is also the same as specific heat capacity. But there is a difference in the mass calculation. Thermal capacity is the energy required to raise the temperature only but not per unit mass. Hence, it will have the units of Calories per Kelvin or Joules per Kelvin.

Thermal capacity will be \[ = 40g \times 0.2\dfrac{{Cal}}{{g.K}}\]

By solving the above equation, the thermal capacity will be \[S = 8Cal/K\].

But, in the given question the units of thermal capacity are Joules per Kelvin.
One calorie can be written as, \[1Cal = 4.184J\]

So, thermal capacity \[S = 8\dfrac{{Cal}}{K}*4.184\dfrac{J}{{1Cal}} = 33.6J/K\]
Therefore, the thermal capacity of \[40g\] of aluminium \[(s = 0.2cal/gK)\] is \[33.6J/K\]
Option d is the answer.

Note:Though both the specific heat capacity and thermal capacity represent the heat energy. The units were different. So, the units must be considered as grams or kilograms is mentioned or not, If the units of mass were mentioned, then it is specific heat capacity.