# An X-ray tube operates at 95 kV with a current of 25 mA and nearly all the electron energy goes...

## Question:

An X-ray tube operates at 95 kV with a current of 25 mA and nearly all the electron energy goes into heat. If the specific heat of the 0.085-kg plate is 0.11 kcal/kg.°C, what will be the temperature rise per minute if no cooling water is used?

## Electric Current

In the field of electro physics, current determines the quantity of passage of particles having some charge from one point to another in a circuit when a potential is generated. Current is quantified in the conventional units of ampere. This movement results in the electricity production.

Given data

• The applied voltage to the x-ray tube is: {eq}{V_a} = 95\;{\rm{kV}} {/eq}.
• The current flowing is: {eq}I = 25\;{\rm{mA}} {/eq}.
• The mass of the plate is: {eq}M = 0.085\;{\rm{kg}} {/eq}.
• The specific heat of plate is: {eq}c = 0.11\;{\rm{kcal/kg}}{\rm{.^\circ C}} {/eq}.

The expression for the power output is,

{eq}p = {V_a}I {/eq}

Substitute the values.

{eq}\begin{align*} p &= \left( {95\;{\rm{kV}}\left( {\dfrac{{1000\;{\rm{V}}}}{{1\;{\rm{kV}}}}} \right)} \right)\left( {25\;{\rm{mA}}\left( {\dfrac{{1\;{\rm{A}}}}{{1000\;{\rm{mA}}}}} \right)} \right)\\ &= 2375\;{\rm{W}} \end{align*} {/eq}

The expression for the temperature rise per minute when no cooling water is used is,

{eq}dT = \dfrac{P}{{Mc}} {/eq}

Substitute the values.

{eq}\begin{align*} dT &= \dfrac{{2375\;{\rm{W}}\left( {\dfrac{{1\;{\rm{J/s}}}}{{1\;{\rm{W}}}}} \right)}}{{\left( {0.085\;{\rm{kg}}} \right)\left( {0.11\;{\rm{kcal/kg}}{\rm{.^\circ C}}\left( {\dfrac{{4184\;{\rm{J}}}}{{1\;{\rm{kcal}}}}} \right)} \right)}}\\ &= 60.71\;{\rm{^\circ C/s}}\left( {\dfrac{{60\;{\rm{s}}}}{{1\;\min }}} \right)\\ &= 3642.6\;{\rm{^\circ C/min}} \end{align*} {/eq}

Thus, the temperature rise per minute when no cooling water is used is {eq}3642.6\;{\rm{^\circ C/min}} {/eq}.