Figure shown two adiabatic vessels, each containing a mass m of water at different temperature. The ends of a metal rod of length L, area of cross section A and thermal conductivity K, are inserted in the water as shown in the figure. Find the time taken for the difference between the temperature in the vessels to become half of the original value. The specific heat capacity of water is s. Neglect the heat capacity of the rod and the container and any loss of heat to the atmosphere.

Answer

A, B

Explanation

`(Q/t)=(KA(T_1-T_2))/(Lms)`
`Rise in temperature in T_2=(KA(T_1-T_2))/(Lms)`
Fall in temperature om
`T_1=(KA(T_1-T_2))/(Lms)`
`Final temperture T_1=T_1-(KA(T_1-T_2))/(Lms)`
`Final temperature T_2=T_2+(KA(T_1-T_2))/(Lms)`
`implies(dT)/(dt)=(2KA(T_1-T_2))/(Lms)`
`impliesIn(T_1-T_2)/(2(T_1-T_2)=(2KA)/(Lms)t`
`In 2=(2KA)/(Lms)t`
`t=(Lms)/(2 KA)In 2`.