Three rods A ,B and C of same length and same cross section area joined. Their thermal conductivities are in ratio 1:2:1.5. If the open ends of A and C are at 200 degree Celsius and 18 degree Celsius respectively the temperature at the junction of A and B in equilibrium is.
Answers
Answer:
116°
Explanation:
3/k(s) = 1/k + 1/2k + 1/3k
∴ k(s) = 18/13 k
( Θ / t ) combined = ( Θ / t ) A
18/13 k x A (200 - 18)/ 3l = k A (200 - Θ) / l
∴ Θ = 116°
The temperature at the junction of A and B in equilibrium is 116°
Three rods A ,B and C of same length and same cross section area joined. Their thermal conductivities are in ratio 1:2:1.5. If the open ends of A and C are at 200 degree Celsius and 18 degree Celsius respectively the temperature at the junction of A and B in equilibrium is.
Let say Thermal conductivity of A, B & C
are K , 2K & 1.5K
Let say temp at junction AB = Tab
Temp at junction BC = Tbc
A = cross section Area
L = Length
K A(200 -Tab)/L = 2K A/(Tab - Tbc)/L
=> 200 - Tab = 2Tab - 2Tbc
=> 3Tab - 2Tbc = 200
2KA(Tab - Tbc)/L = 1.5KA(Tbc - 18)/L
=> 2Tab - 2Tbc = 1.5Tbc - 27
=> 3.5Tbc - 2Tab = 27
3Tab - 2Tbc = 200
10.5Tab - 7Tbc = 700
3.5Tbc - 2Tab = 27
7Tbc - 4Tab = 54
6.5Tab = 754
=> Tab = 116