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 T _{1}, T_{2}, and T_{3} 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) (T _{1}+ T_{2} +T_{3})/3 (b) (T_{1}** –

**T**

_{2}+T_{3})/3 (c) 2(T_{1}**+ T**

_{2})/3**(d) T**

_{2}^{ }(e) T_{3}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 T_{3}.

**(2)** **Equal masses of three liquids A, B,and C with specific heats c _{1}, c_{2} and c_{3 }at temperatures t_{1}, t_{2} and t_{3} (all in degree Celsius) respectively are thoroughly mixed. The resulting temperature is**

**(a) (c _{1}t_{1} + c_{2}t_{2}^{ }+ c_{3}t_{3})/3**

**(b) (c _{1}t_{1} + c_{2}t_{2}^{ }+ c_{3}t_{3})/(c_{1} + c_{2}^{ }+ c_{3})**

**(c) 3(c _{1}t_{1} + c_{2}t_{2}^{ }+ c_{3}t_{3})/(c_{1} + c_{2}^{ }+ c_{3})**

**(d) 3(t _{1} + t_{2}^{ }+ t_{3})/(c_{1} + c_{2}^{ }+ c_{3})**

**(e) (t _{1} + t_{2}^{ }+ t_{3})/ (c_{1} + c_{2}^{ }+ c_{3}) **

The initial heat content is (mc_{1}t_{1} + mc_{2}t_{2}^{ }+ mc_{3}t_{3}) where ‘m’ is the mass of each liquid.** **

The final heat content is (mc_{1} + mc_{2} + mc_{3})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 = (c_{1}t_{1} + c_{2}t_{2}^{ }+ c_{3}t_{3})/(c_{1} + c_{2}^{ }+ c_{3})** **

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