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

Options

A. `40^(@)C`
B. `50^(@)C`
C. `60^(@)C`
D. `70^(@)C`

Answer

A

Explanation

Let `theta` be temperature of interface.
`therefore (K_(P)A(100-theta))/(l)=(K_(Q)A(theta-0))/(l)`
`therefore (K_(P))/(K_(Q))=(theta)/(100-theta) rArr (2)/(3)=(theta)/(100-theta)`
or, `200-2theta=3theta or, 5theta=200 or, theta=40^(@)C`