Question

In an X-Ray tube if electrons are accelerated through 140kV then anode current obtained is 30mA. If the whole energy of electrons is converted into heat than the rate of production of heat at anode will be:
A. 968 calorie
B. 892 calorie
C. 1000 calorie
D. 286 calorie

Answer 1

Hint: Whenever a charge is accelerated through some potential difference, it gains the energy in form of kinetic energy which can be converted into heat energy. In the question, it is given that whole energy gets converted to heat energy, hence we can directly say, the energy gained due to potential difference goes to heat generation.

Formula used:
Energy (E) = V q

Complete step-by-step answer:
Given, the current in the circuit is 30mA. That means the charge flown in 1 sec will be 30mC. Since all the energy associated with the potential difference gets converted to heat, hence energy associated with the potential energy is:
$E = V q$
$E = 140 k \times 30 m$
$E = 140 \times 10^3 \times 30 \times 10^{-3}$
$E = 140 \times 30 = 4200 J$
This is the kinetic energy obtained by the electrons in 1 sec, which goes directly into heat energy at the anode. Hence the heat obtained at the anode = 4200 J
 $\dfrac{4200}{4.2} = 1000 \ cal$ ……..[ as 1 calorie = 4.2 joules ]

So, the correct answer is “Option C”.

Additional Information: One might wonder how come a current could be generated inside an empty tube, where there is not even matter present. This is because of two main reasons. First of all the metal used has very less ionization energy and secondly the potential difference applied is huge!

Note: It is very important for the students to act by seeing the options. As in the options, heat is given in the form of calorie, hence we must convert the heat to calorie. Also, the calculated heat is Joules because the S.I. The unit of heat and energy is Joule. Here, we are not given the time for which we have to calculate the heat generated hence one should proceed by finding the values per unit time.