Question

The temperature of hot and cold end of a 20 cm long rod in thermal steady state are at ${{100}^{{}^\circ }}C$ and ${{20}^{{}^\circ }}C$ respectively. Temperature at the centre of the rod is:
(A) ${{50}^{{}^\circ }}C$
(B) ${{60}^{{}^\circ }}C$
(C) ${{40}^{{}^\circ }}C$
(D) ${{30}^{{}^\circ }}C$

Answer 1

We know that the measure of the ability of a substance, or more generally of any physical system, to transfer heat energy to another physical system. The temperature of a substance is closely related to the average kinetic energy of its molecules. Celsius is currently a derived unit for temperature in the SI system, kelvin being the base unit. ${{0}^{{}^\circ }}C$ The two main reference points of the Celsius scale were the freezing point of water (or melting point of ice) being defined as ${{0}^{{}^\circ }}C$ and the boiling point of water being ${{100}^{{}^\circ }}C$.

Complete step by step solution:
Let us start the answer by the diagram for this question:

Now we have to form the expression from the values that are mentioned in the given question:
Let us first write that:
${{H}_{1}}+{{H}_{2}}=0$
Now we have to form the equation involving the temperature variables:
$\dfrac{\Delta {{T}_{1}}}{{{R}_{1}}}+\dfrac{\Delta {{T}_{2}}}{{{R}_{2}}}$
Now after the evaluation we get that:
$\dfrac{\Delta {{T}_{1}}}{{{R}_{1}}}+\dfrac{\Delta {{T}_{2}}}{{{R}_{2}}}=0$
$\Rightarrow \dfrac{T-20}{{{R}_{1}}}+\dfrac{T-100}{{{R}_{2}}}=0$
$\Rightarrow T-20+T-100=0$
So, the final temperature is given as
$T=\dfrac{120}{2}=60$
Hence, the temperature at the centre of the rod is ${{60}^{{}^\circ }}C$.

So, the correct answer is option B.

Note: We know that the human body reacts to external and internal changes. Body temperature rises when the external temperature increases but also when the internal temperature increases. When temperatures rise, the body reacts by increasing blood flow to the skin's surface, taking the heat from within the body to the surface. This means sweat. As the sweat evaporates, the body cools down.
It should be known to us that when our body temperature drops, our heart, nervous system and other organs can't work normally. Left untreated, hypothermia can lead to complete failure of our heart and respiratory system and eventually to death. Hypothermia is often caused by exposure to cold weather or immersion in cold water.