Question

Four identical rods of the same material are joined at ends so as to form a square. If the temperature difference at the ends of a diagonal is ${{100}^{\circ }}C$, then the temperature difference across the ends of another diagonal will be
A. ${{0}^{\circ }}C$
B. ${{25}^{\circ }}C$
C. ${{50}^{\circ }}C$
D. ${{100}^{\circ }}C$

Answer 1

Hint: We have given four identical rods which are joined to form a square and we have to find the temperature difference across the diagonals. As we know heat will be transferred due to temperature difference and heat flows from higher temperature to lower temperature. So by using the difference in the temperature , we are able to find the temperature difference.

Complete step by step solution:
Let the four identical rods be A,B,C and D which have AC and BD as a diagonal point. We are asked to find the temperature difference between points B and D, which is ${{T}_{B}}-{{T}_{D}}$.
Consider the temperature at A = ${{T}^{\circ }}C$
Therefore, temperature at C = $t+{{100}^{\circ }}C$
As heat is conducted from A to C via B or D. B and D lie midway along with the passing of heat conduction through ABC and ADC respectively.
Hence temperature of B = \[\dfrac{t+(t+100)}{2}\] = $t+{{50}^{\circ }}C$
Similarly temperature of D = \[\dfrac{t+(t+100)}{2}\] = $t+{{50}^{\circ }}C$
So the temperature difference across the ends of another diagonal will be ${{0}^{\circ }}C$.

Hence, option A is the correct answer.

Note: By conduction, we mean the transfer of energy when one of the parts of an object is heated and it gets excited and transfers energy to its nearest particle, which further transmits the energy and with this process, heat energy gets transferred from one end to another.