Three rods of same dimensions have thermal conductivities 3K, 2K and K respectively. |
They are arranged as shown below |
What will be the temperature T of the junction? |
A) \[\frac{200}{3}\,{{\,}^{o}}C\]
B) \[\frac{100}{3}\,{{\,}^{o}}C\]
C) \[75\,{{\,}^{o}}C\]
D) \[\frac{50}{3}{{\,}^{o}}C\]
Correct Answer: A
Solution :
[a]: Let L and A be length and area of cross- section of each rod. At steady state,\[{{H}_{1}}={{H}_{2}}+{{H}_{3}}\] \[\frac{(100-T)(3K)A}{L}=\frac{(T-50)2KA}{L}+\frac{(T-0)KA}{L}\] \[3(100-T)=2(T-50)+T\] \[300-3T=2r-100+T\] \[6T=400\]or\[T=\frac{400}{6}=\frac{200}{3}{{\,}^{o}}C\]You need to login to perform this action.
You will be redirected in
3 sec