Question

A pot with a steel bottom 1.2 cm thick rests on a hot stove. The area of the bottom of the pot is 0.150$m^2$. The water inside the pot is at 100$^ \circ C$ and 0.440 kg is evaporated every 5.0 minute. Find the temperature of the lower surface of the pot, which is in contact with the stove. Take LV =2.256×106 J/kg and ksteel =50.2W/m−K(in C).

Answer 1

Applying flow of heat energy over time it means, we can calculate heat change at smaller and smaller time intervals. Substituting given values in the formula we can find the temperature of the lower surface of the pot which is in contact with the stove.

Formula used:
$\dfrac{{dQ}}{{dt}} = \dfrac{{KA}}{L}\Delta T$

Complete Step by step solution:
Consider , The heat flow from the stove is used to convert water to steam.
\eqalign{ & \dfrac{{dQ}}{{dt}} = \dfrac{{0.44\left( {2.256 \times {{10}^6}} \right)}}{{5\left( {60} \right)}} \cr & \Rightarrow \dfrac{{dQ}}{{dt}} = \dfrac{{0.99264}}{{300}} \cr & \therefore \dfrac{{dQ}}{{dt}} = 3309J/\sec \cr}
Now, $\dfrac{{dQ}}{{dt}} = \dfrac{{KA}}{L}\Delta T$
Where, Q is the small amount of heat transferred over a time dt.
dt is the small amount of time over which dQ was transferred.
K is the thermal conductivity of the material
A is the cross-sectional area of the object.
$\Delta$T is the temperature difference between the warmest and coldest temperatures in the material.
L is the length across which the heat is being transferred.
Substitute given values in the formula.
\eqalign{ & \dfrac{{dQ}}{{dt}} = \dfrac{{50.2\left( {0.15} \right)}}{{0.012}}\left( {T - 100} \right) \cr & \Rightarrow 627.5\left( {T - 100} \right) = 3309 \cr & \therefore T = 105.27{}^ \circ C \cr}

Hence, the correct option is 105.27 ${}^ \circ C$.

Additional information:
Definition of Thermal conductivity is the rate at which heat is transferred by conduction through a unit of cross-section area of a material when a temperature gradient exists perpendicular to the area.
Hydrogen gas and helium gas are distinguished among gases for the highest thermal conductivity.
The diamond is material which leads thermally conductive material and has conductivity values measured higher than copper.
Generally, good conductors of electricity are metals like copper, aluminum, gold, and silver. These are also good heat conductors, whereas insulators of electricity are wood, plastic, and rubber these are poor heat conductors.

Note:
The heat energy is the rate at which heat is transferred over time, its SI unit of heat current is joule per second or watt (W). Remember those formulas which are related to heat energy. We Used for detecting heat energy i.e variable H to represent heat current.