Transmission Of Heat Question 59
Question: Two cylinders P and Q have the same length and diameter and are made of different materials having thermal conductivities in the ratio 2 : 3. These two cylinders are combined to make a cylinder. One end of P is kept at 100°C and another end of Q at 0°C. The temperature at the interface of P and Q is
[MP PMT 1994; EAMCET 2000]
Options:
A) $ 30^{o}C $
B) $ 40^{o}C $
C) $ 50^{o}C $
D) $ 60^{o}C $
Show Answer
Answer:
Correct Answer: B
Solution:
Temperature of interface $ \theta =\frac{K _{1}{\theta _{1}}+K _{2}{\theta _{2}}}{K _{1}+K _{2}} $ where K1 = 2K and K2 = 3K $ ( \because ,\frac{K _{1}}{K _{2}}=\frac{2}{3} ) $
Therefore $ \theta = $
$ \frac{2K\times 100+3K\times 0}{2K+3K} $
$ =\frac{200K}{5K}=40{}^\circ C $
BETA
