Question

Four rods with different radii r and length l are used to connect two heat reservoirs at different temperatures. Which one will conduct most heat?
(a) r = 1 cm, l = 0.5 m
(b) r = 2 cm, l = 0.5 m
(c) r = 1 cm, l = 1 m
(d) r = 1 cm, l = 1 m

Answer 1

The different length and radii of rods will heat at different temperatures. Heat conduction is a method of transfer of heat between two objects in direct contact with each other. The temperature will determine which one will conduct the most of the heat and temperature also defines the flow of heat in a particular direction.

Complete answer:
The good conductors of electricity (metals like copper, aluminium, gold, and silver) also are good heat conductors, whereas insulators of electricity (wood, plastic, and rubber) are poor heat conductors. Let the molecules in the bodies be different temperatures. The (average) K.E. of a molecule within the hot body is above within the colder body. If two molecules collide, an energy transfer from the recent to the cold molecule occurs. The cumulative effect from all collisions leads to a net flux of warmth from the recent body to the colder body. The warmth flux thus depends on the temperature difference .This Difference in temp. = Temperature (hot body) - Temperature (cold body).
Since According to Thermal Conductivity,

& H=\dfrac{KAd\theta }{L} \\\ & \Rightarrow H\propto \dfrac{A}{L}\alpha \dfrac{\pi {{r}^{2}}}{L} \\\ \end{aligned}$$ Put all the four options individually we get, $$\begin{aligned} & a)H={{(\dfrac{A}{L})}_{1}}=\dfrac{\pi {{(1)}^{2}}}{0.5}=2\pi \\\ & b)H={{(\dfrac{A}{L})}_{2}}=\dfrac{\pi {{(2)}^{2}}}{0.5}=8\pi \\\ & c)H={{(\dfrac{A}{L})}_{3}}=\dfrac{\pi {{(1)}^{2}}}{1}=\pi \\\ & d)H={{(\dfrac{A}{L})}_{4}}=\dfrac{\pi {{(2)}^{2}}}{2}=2\pi \\\ \end{aligned}$$ Hence, for option B where the rod with radius r = 2 cm, and length L = 0.5 m will conduct the most heat. The heat transfer depends on different factors like material, length and radii or area of cross section. Hence the rod with greater radius and least length will conduct maximum heat. Conversely, if the temperatures are an equivalent, total heat transfer rate falls to zero, and equilibrium is achieved. Due to the very fact that the amount of collisions increases with increasing area, heat conduction depends on the cross-sectional area. If you touch a chilly wall together with your palm, your hand cools faster than if you only touch it together with your fingertip. A third thing about the mechanism of conduction is the thickness of the fabric through which heat transfers. **Option B is correct.** **Note:** You get a more severe burn from boiling water than from hot water, because the phenomena of heat transfer. The SI unit for heat will be Joule (J) and C.G.S. the unit for heat should be calorie. Calorie and Joule are related to each other by a factor of 4.18.Calorie is defined as the amount of heat requires raising the temperature of 1 gm of water by 1 degree Celsius.