Q. 37

Two bodies of masses m1 and m2 and specific heat capacities s1 and s2 are connected by a rod of length ℓ, cross-sectional area A, thermal conductivity K and negligible heat capacity. The whole system is thermally insulated. At time t = 0, the temperature of the firs body is T1 and the temperature of the second body is T2(T2> T1). Find the temperature difference between the two bodies at time t.

Answer :


Masses of body = m1 and m2

Specific heat capacities = s1 and s2

Rod of length= ℓ,

Cross-sectional area = A

Thermal conductivity = K

Rate of transfer of heat from the rod is given by –


Where,= temperature of first and second body.

A= Area of cross section of the

K = thermal conductivity of the

L= length

Heat transfer from the rod in time ∆t –

∆Q= (2)

Heat loss by the body at temperature T2 is equal to the heat gain by the body at temperature T1.

Heat loss by the body at temperature T2 in time ∆t is –

∆Q=m2s2 (T2′-T2) (3)

From (1) and (2)

m2s2 (T2′-T2) =

T2’=T2- ∆t

This is the fall in the temperature of the body at temperature T2.

Similarly, rise in temperature of water at temperature T1 is –

T1’=T1+ t

Change in the temperature


= T2- ∆t - T1- t

{(T2′-T1′)-(T2-T1)}=- ∆t - t

= -

Where is the rate of change of temperature difference

∆T= )

Integrating both the sides -


ln |T2-T1| = -

Taking the anti-log




Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Work done in Thermodynamic ProcessFREE Class
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses