Question

the temperature at the ends of a uniform rod of length 100 cm respectively 95 degree centigrade and 5 degree centigrade what will be the temperature at a point 30 cm far from the hotter end and also calculate the temperature gradient​

Answer 1

Answer:

The temperature at a point 30cm far from the hotter end is 68°c

Explanation:

Answer 2

Given :

Length of the rod :

= 100 cm

Temperature at the ends of the rod :

95°C and 5°C

To Find :

Temperature at a distance of 30 cm from hotter end and also the temperature gradient = ?

Solution :

Let's divide the rod in two sections , 1st section is from A to P where a is the end whose temperature is 95°C  and the 2nd section is from P to B where B is the end whose temperature is  5°C.

So, we have Δ$H_{1} =$ Δ$H_{2}$

where ΔH = Heat passed through corresponding section

$\frac{\alpha \Delta T_{1} A_{1}}{L_{1}}= \frac {\alpha \Delta T_{2} A_{2}} {L_{2}}$

Here , $A_{1}$ and $A_{2}$ are cross sectional areas which are equal

 $\alpha$ = heat conduction constant

So,

    $\frac{\Delta T_1}{L_1} = \frac{\Delta T_2}{L_2}\\\\\frac{95 - T}{30} = \frac{T-5}{70}$

Here T is the temperature at point P

$(95- T) \times 70 = 30 \times (T-5)\\665 - 7T = 3T - 15 \\10T = 680\\T = 68$

So temperature at point P is 68° C.

Now for temperature gradient :

= $\frac{\Delta T _{along rod}}{length of rod}$

$= \frac{95 \degree - 5 }{100}$ °C per cm

=$\frac{90}{100}$  °C per cm

= 0.9 °C per cm

So the temperature gradient is 0.9 °C per cm .