## Saturday, May 12, 2007

### Two Questions (MCQ) from Thermal Physics

The following simple questions are for checking whether you have understood certain fundamental principles in Thermal Physics:

(1) Three bodies A, B, and C with thermal capacities in the ratio 1:2:3 are at temperatures T1, T2, and T3 respectively. When A and B are kept in contact, the common temperature is T. When A, B and C are kept in contact, the common temperature is T itself. Then T is equal to

(a) (T1+ T2 +T3)/3 (b) (T1 T2 +T3)/3 (c) 2(T1 + T2)/3 (d) T2 (e) T3

Simple questions often make even fairly intelligent students commit mistake and this is one such question.

The crucial point you must note is that the common temperature of A and B is unchanged when C also is kept in contact with them. So, the common temperature of A and B must be the same as the temperature of C which is T3.

(2) Equal masses of three liquids A, B,and C with specific heats c1, c2 and c3 at temperatures t1, t2 and t3 (all in degree Celsius) respectively are thoroughly mixed. The resulting temperature is

(a) (c1t1 + c2t2 + c3t3)/3

(b) (c1t1 + c2t2 + c3t3)/(c1 + c2 + c3)

(c) 3(c1t1 + c2t2 + c3t3)/(c1 + c2 + c3)

(d) 3(t1 + t2 + t3)/(c1 + c2 + c3)

(e) (t1 + t2 + t3)/ (c1 + c2 + c3)

The initial heat content is (mc1t1 + mc2t2 + mc3t3) where ‘m’ is the mass of each liquid.

The final heat content is (mc1 + mc2 + mc3)t where ‘t’ is the common temperature after mixing. [We have taken the reference heat energy level at zero degree Celsius].

Equating these two, we obtain t = (c1t1 + c2t2 + c3t3)/(c1 + c2 + c3)