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)