Question

50g of metal piece at ${27^o}$C requires 2400 J of heat energy so as to attain a temperature of ${327^o}$C. Calculate the specific heat capacity of the metal.

Answer 1

- Hint: In this question use the direct relation between the heat energy required to attain the specific temperature, mass of metal, specific heat capacity of the metal and the change in temperature that is $H.E = m \times s \times \Delta T$. The change in temperature can easily be obtained by the difference of the initial temperature to that with the final temperature that is to be achieved.

Complete step-by-step solution -

Given data:
Weight of metal piece = 50gm
Temperature at which the metal piece has = ${27^o}$C
Heat energy (H.E) required = 2400 J
To attain a temperature of ${327^o}$C
So the change in temperature of the metal piece is, $\Delta T$ = 327 – 27 = ${300^o}$C
Let the specific heat of the metal be s.
So the heat energy required to attain the temperature of ${327^o}$C is the product of mass of the metal piece, specific heat capacity of the metal piece and the change in temperature of the metal piece.
Therefore, heat energy = mass $ \times $ specific heat $ \times $ change in temperature.
$ \Rightarrow H.E = m \times s \times \Delta T$
Now substitute all the values in the above equation we have,
$ \Rightarrow 2400 = 50 \times s \times 300$
Now simplify this we have,
\[ \Rightarrow \dfrac{{2400}}{{50 \times 300}} = s\]
\[ \Rightarrow s = \dfrac{8}{{50}} = 0.16\] J/gm-${^o}$C
So this is the required specific heat capacity of the metal.

Note – It is very important to understand the basics of specific heat capacity as it helps solving problems of this kind. Specific heat capacity is defined as the amount of the heat energy which gives rise to one degree Celsius increase in temperature per unit mass of the substance whose specific heat capacity is to be obtained. Molar heat capacity need not be confused with specific heat capacity as both are different. Molar heat capacity is concerned with one mole of the substance.