What is the Temperature Difference Between Two Bodies Connected by a Rod?

[aviravir1]

Two bodies of masses m1 and m2 and specific heat capacities s1and s2 are connected by a rod of length L crossectional area A,thermal conductivty K and negligible heat capacity.The whole system is thermally insulated.At time t=0 the temperature of the first body is T1and the temperature of second body is T2(T2>T1).Find the temp. difference betw. 2 bodies at time t.

 

[ideasrule]

What relevant equations did you learn? What attempt did you make at solving this question?

 

[aviravir1]

well actually i m not able to move an inch in it...

can u please give me some solid hint so that i can proceed..

 

[aviravir1]

please help...giv some hint ...how shud i proceed

 

[aviravir1]

why no one is replying...atleast give some hint how to do it..so that i may proceed...

 

[ideasrule]

The rate of heat transfer, given by H=kA*delta-T/delta-x, is equal to mc*dT/dt for both objects connected by the rod, only one rod's temperature goes down while the other's goes up. Depending on whether your class is calculus-based, you can either calculate the power transferred in time t and set it equal to mc*delta-T for both objects, or you can use calculus to get a more accurate solution.

 

[aviravir1]

actually i did lik this(see the attachment)

firstly is it correct

secondly wen i tried integrating it its not giving the ans.

 

[aviravir1]

please help

 

[aviravir1]

please help...i m in dire need

im getting ans as (T₂-T₁)e^(1-f)t

wer f=KA(m1s1+m2s2)/(L(m1s1m2s2))

wer as ans is (T₂-T₁)e^-ft

wer f=KA(m1s1+m2s2)/(L(m1s1m2s2))