Answer:
The temperature of the bar at a point 0.215m from the hot end is 286°C
Explanation:
To solve this problem it is necessary to take into account the concepts related to the rate of heat conducted through objects.
Heat flow rate is the amount of heat that is transferred per unit of time in some material,
The formula is given by
[tex]\frac{\Delta Q}{\Delta t} = kA\frac{\Delta T}{\Delta x}[/tex]
Where,
[tex]\Delta Q =[/tex] is the net heat transfer
[tex]\Delta t=[/tex] is the necessary time
[tex]\Delta T =[/tex] is the temperature difference between the cold and hot sides
[tex]\Delta x =[/tex] is the thickness of the material that conducts heat
k= is the thermal conductivity
A = Cross-sectional area
In our defined values we have to,
[tex]\frac{\Delta Q}{\Delta t} = 2.23J/s[/tex]
[tex]k_{brass} = 109W/m\°C[/tex]
[tex]A= 2.16*10^{-4}m^2[/tex]
[tex]x= 0.215m[/tex]
[tex]\Delta T =(306\°C-T_c)[/tex]
Replacing the values at the equation,
[tex]2.23 = (109)(2.16*10^{-4})\frac{(306-T_c)}{0.215}[/tex]
[tex]\frac{(2.23)(0.215)}{(109)(2.16*10^{-4})}=(306-T_c)[/tex]
[tex]T_c = \frac{(2.23)(0.215)}{(109)(2.16*10^{-4})}-306[/tex]
[tex]T_c = 286\°C[/tex]
Therefore the temperature of the bar at a point 0.215m from the hot end is 286°C
