$1 \mathrm{Kcal}$ of heat flowing through a rod of iron. When the rod is cut down to 4 pieces then what will be the heat flowing through each piece having same differential temperature?

• A

  $1 / 2 \mathrm{Kcal}$
• B

  $1 / 4 \mathrm{Kcal}$
• Correct answer
  C

  $1 \mathrm{Kcal}$
• D

  $1 / 15 \mathrm{Kcal}$.

Solution

We know that the heat flowing through a conductor is given by $$ \begin{aligned} \frac{Q}{t} & =-K A\left(\frac{d \theta}{d x}\right) \\ \Rightarrow Q & =-K A\left(\frac{d \theta}{d x}\right) t \end{aligned} $$
Where $$ \begin{aligned} K & =\text { thermal conductivity of the material } \\ A & =\text { area of cross-section } \\ \frac{d \theta}{d x} & =\text { temperature gradient } \\ t & =\text { time } \end{aligned} $$ Now if we cut the rod into 4 pieces, $A$ remains same $K$ remains same, $\frac{d \theta}{d x}$ is said to be same, so for same time $t, Q$ is going to be same as earlier.

Hence, the correct answer is option: 'C'.