91影视

i. Two rods are identical.

ii.Temperature on the left side,$T_1=0掳\text{C}$

iii. Temperature on the right side,$T_2=100掳\text{C}$

iv. The energy transferred in conduction is$10\text{J}$

v. The time of rate of conduction,$t=2.0\text{min}$

The heat transfer from a hotter body to a colder body is defined as the process of conduction and this heat transfer is known as thermal conduction.Using the formula for conduction rate, we can write for the ratio of conduction rates for arrangements (a) and (b) that are directly proportional to the area of the material and inversely to the length. From this, we can find the time required to conduct 10 J if the rods were welded side to side.

Formula:

The rate at which the sphere emits thermal radiation, $P_{cond}=\frac{kA\left(螖T\right)}{L}$ 鈥�(颈)

Where,$k$is the thermal conductivity of the material,$A$is the surface area of radiation,$螖T$is the temperature difference of the two ends,$L$is the length of the conduction.

Since the rods are identical and havethesame temperature difference in both arrangements shown in the figure (a) and (b), conduction rate is given using equation (i) as:

$P_{cond}鈭�\frac{A}{L}$

Hence, the rate change at left and right sides is given as:

$\begin{array}{c}\frac{P_{cond,b}}{P_{cond,a}}=\frac{A_b}{A_a}脳\frac{L_a}{L_b}\\ =2脳2\\ =4\\ P_{cond,b}=4P_{cond,a}\end{array}$

Sincetheconduction rate of arrangement (b) is greater than the conduction rate of arrangement (a), the time required to conduct 10 J if the rods were welded side to side is given as:

$\begin{array}{c}{t}^{\text{'}}=\frac{2\text{鈥尘颈苍}}{4}\\ =0.50\text{min}\end{array}$

Hence, the value of the required time is$0.50\text{min}$