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Two metal rods made up of iron (K1=79Wm^...

Two metal rods made up of iron `(K_1=79Wm^(-1)K^(-1))` and brass `(K_2=109Wm^(-1)K^(-1))` are of identical shape and size. These are fused at the junction. If the temperature at the free end of iron is at a steam point and brass at ice point then calculate the temperature at the junction, when the steady state is attained.

Text Solution

Verified by Experts

Given `A_(1)=A_(2),l_(1)l_(2)=l, K_(t)=79 Wm^(-1)K^(-1)`
`K_(2)=109 Wm^(-1)k^(-1), theta_(1)=373 K, theta_(2)=273 K, theta = ?`
Since `theta_(1) theta_(2)`
`(K_1 A(theta_1-theta_2)t)/(l_1)=(K_2A(theta-theta_2)t)/(l_2)" " therefore K_(1)(theta_1- theta)= K_2 (theta- theta_2)`
`rarr 79(373- theta)= 109(theta - 273) rarr 29-79 theta = -1090-29757`
ie 1880= 59224 `rarr therefore theta =(59224)/(188)=315.02`
`therefore` temperature of the junction is 315.02 K
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