Question

An electrical heater is kept in vacuum and is heated continuously by passing electric current. Its temperature:
(A) Will go on rising with time
(B) Will stop after sometime as it will lose heat to the surroundings by conduction
(C) Will rise for some time and thereafter will starts falling
(D) Will become constant after some time because of loss of heat due to radiation

Answer 1

We know that in case of any electrical device, there is always a resistance present in it. When voltage is applied to it that means when the heater is kept in condition for some time, we will see that it becomes hot. This means that its temperature has risen.

Complete Step-By-Step Solution:
We know that when voltage is applied to the electrical heater, the current starts flowing in it. Due to this current a power is generated.
Let us consider current $i$be flowing inside the device.
As discussed earlier, let the resistive element of magnitude $R$be present. Thus, the power developed in the heater is given by, $P = {i^2}R$
Now, this value is constant, so the output remains constant as long as the input power remains constant.
We know, heat developed in the device is given by the product of power and time.
Now, we know initially the temperature as well as the radiation keeps on rising. But after a certain point in time the radiation becomes equal to the input power and so the temperature stops rising.
Thus, we can say energy was initially dissipated in the form of heat, so temperature was rising, but after some time energy started dissipating in the form of radiation, hence temperature becomes constant.’

Therefore, option (D) will become constant after some time because of loss of heat due to radiation is correct.

Note:
We know, heat developed in the device is given by the product of power and time.
Thus, heat generated becomes:
$H = Pt$
Thus, we can write:
$H = {i^2}Rt$