Question

An iron ball at ${40^ \circ }C$ is dropped in a mug containing water at ${40^ \circ }C$.
The heat will
A. flow from iron ball to water
B. not flow from iron ball to water or from water to iron ball
C. flow from water to iron ball
D. increase in temperature of both.

Answer 1

Hint:This problem is based on Newton’s Law of Cooling. Newton’s Law of Cooling states that: the rate of heat loss of a body is directly proportional to the difference in the temperatures between the body and its surroundings. In mathematical form,
\[Q = hA\left( {T - {T_0}} \right)\]
where Q = heat energy transferred, h = heat transfer coefficient, A = area of heat transfer and $T\& {T_0}$ are the temperature of the body and temperature of the surroundings respectively.

Complete step-by-step answer:
Consider an iron ball at ${40^ \circ }C$ dropped in the mug of water at the temperature of ${40^ \circ }C$.
Let us apply Newton's law of cooling for the iron ball.
 \[Q = hA\left( {T - {T_0}} \right)\]
where Q = heat energy transferred, h = heat transfer coefficient, A = area of heat transfer and $T\& {T_0}$ are the temperature of the body and temperature of the surroundings respectively.
Newton's law of cooling basically says that the higher the temperature difference between the body and the surroundings, the higher is the rate of heat transfer.
Here,
Temperature of the iron ball, $T = {40^ \circ }C$
Temperature of the surroundings (here, the mug of water), ${T_0} = {40^ \circ }C$
Applying this in the equation, we get –
\[
  Q = hA\left( {T - {T_0}} \right) \\
  Q = hA\left( {40 - 40} \right) = 0 \\
 \]
Here, we see that there is no heat flow from the iron ball also, if we reverse the $T\& {T_0}$ to consider the transfer of heat from the water to iron ball, we get the same answer i.e. Q=0.

Hence, the correct option is Option B.

Note: This problem can also be explained with the concept of Zeroth’s law of thermodynamics. The Zeroth’s law states that –
If two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.
The criterion for deciding that two systems are in equilibrium, is the temperature. If two systems are in equilibrium, there is zero heat transfer among them and they have the same temperature.
Here, we can say that the iron ball and mug of water are in thermal equilibrium with each other, and hence, there is no net flow of heat from either of them.