Respuesta :
Answer:
The total number of small cylinder = 7.
Explanation:
Lets take
Radius of the large cylinder = R
length = L
L = 10 R
The total area A = 2 π R² + π R L
The length of the small cylinder = l
The number of small cylinder = n
L = n l
The total area of small cylinders
A'=n (2 π R² + π R l)
As we know that emissive power given as
P = A ε σ T⁴
For large cylinder
P = A ε σ T⁴ -----------1
For small cylinders
P'=A' ε σ T⁴ ------2
From 1 and 2
Given that
P'= 2 P
A' ε σ T⁴ =2 A ε σ T⁴
A'=2 A (All others are constant)
n (2 π R² + π R l) =(2 2 π R² + π R L)
n (2 R² + R l) = (2 R² + R L)
[tex]n(2R^2+R\times \dfrac{L}{n}) = 2(2R^2+RL)[/tex]
L = 10 R
[tex]n(2R^2+R\times \dfrac{10R}{n}) =2 (2R^2+R\times 10R)[/tex]
[tex]n(2+\dfrac{10}{n}) =2( 2+ 10)[/tex]
2 n +10 = 2 x 12
2 n +10 = 24
2 n = 24 -10
2 n = 14
n = 7
The total number of small cylinder = 7.
Emissive power of a body is defined as the total amount of thermal energy emitted by the body per unit are per unit time for all possible wavelength.The total number of smaller cylinder is 7.
Given information-
The length of the solid cylinder is 10 times its radius.
The temperature of the small cylinder is equal to the original cylinder.
The total radiant power emitted by the pieces is twice that emitted by the original cylinder.
What is emissive power?
Emissive power of a body is defined as the total amount of thermal energy emitted by the body per unit are per unit time for all possible wavelength.
It can be given as,
[tex]E=\sigma\varepsilon AT^4[/tex]
As the total radiant power emitted by the pieces is twice that emitted by the original cylinder. Thus,
[tex]2\sigma\varepsilon AT^4=\sigma\varepsilon A'T^4[/tex]
Here, A is the surface area of the original cylinder and A' is the surface area of the small cylinder,
Cancel all the constant values,
[tex]2A=A'[/tex]
Let [tex]n[/tex] be the total number of small cylinder, thus,
[tex]2(2\pi R^2+\pi RL)=n\times(2\pi R^2+\pi Rl)[/tex]
Here [tex]l[/tex] is the height of the small cylinder and [tex]L[/tex] is the length of the large cylinder.
[tex]2 R^2+ RL=n\times(2 R^2+Rl)[/tex]
The length of the original cylinder is n times the length of the small cylinder. Thus,
[tex]2 R^2+ RL=n\times(2 R^2+R\dfrac{L}{n} )[/tex]
As the length of the solid cylinder is 10 times its radius. Thus,
[tex]2 R^2+ R\times10R=n\times(2 R^2+R\dfrac{10R}{n} )\\2+10=n(2+\dfrac{10}{n} )\\2n+10=24\\n=\dfrac{14}{2}\\ n=7[/tex]
Hence the total number of smaller cylinder is 7.
Learn more about the emissive power here;
https://brainly.com/question/1278030
