Question

Two diagonally opposite corners of a square made of four thin rods of the same material, same dimensions are at a temperature of ${40^ \circ }C$ and ${10^ \circ }C$ . If only heat conduction takes place, then the temperature difference between the other two corners will be
A. ${0^ \circ }C$
B. ${10^ \circ }C$
C. ${25^ \circ }C$
D. ${15^ \circ }C$

Answer 1

Hint:Relate the question with flow of electric current. This question can be solved by converting the formula for heat flow to current and relating the similar quantities. Since all four rods are made of the same material and dimensions, the heat conductivity is the same for all four rods. However, this question can easily be solved by using logic without any calculations.

Complete answer:
Since all four rods are made up of the same materials and dimensions, their heat conductivity is the same for all four rods.This question can be solved by calculating assuming the known terms and finally calculating the temperatures of the leftover corners and then finding the temperature difference. But an easy way to do this is given below

Since the heat conductivity is the same, the temperature drop for every rod is the same. Hence the temperature of the other two corners will be the same. Thus the difference in temperature of the other two corners is zero.

Hence option A is the correct answer.

Additional information:
According to thermodynamic systems, heat transfer is defined as the movement of heat across the border of the system due to a difference in temperature between the system and its surroundings.Interestingly, the difference in temperature is said to be a ‘potential’ that causes the transfer of heat from one point to another. Besides, heat is also known as flux.

Note:Students should learn to use such logics for ease of calculations. These can decrease the time needed for solving a problem which is good in competitive exams. Also, if the dimensions of the rods or the material are different, this method will not work.