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Concepts Of Physics MCQ Edition [Volume 2]PhysicsCalorimetry

Three different liquids A , B , and C have temperatures of 12^ C , 19^ C , and 28^ C respectively, for equal masses. The temperature when A and B are mixed is 16^ C , while mixing B and C yields a temperature of 23^ C . Determine the temperature when A and C are mixed.

Options

  1. A19.5^ C
  2. B21.2^ C
  3. C20.3^ C
  4. D20.0^ C

Correct answer

C. 20.3^ C

Step-by-step solution

Let the specific heat capacities of liquids A , B , and C be s_A , s_B , and s_C respectively. Let the mass of each liquid be m . When liquids A and B are mixed, the equilibrium temperature is 16^ C . By the principle of calorimetry, heat gained by A equals heat lost by B : m s_A (16 - 12) = m s_B (19 - 16) 4 s_A = 3 s_B s_A = 3 4 s_B When liquids B and C are mixed, the equilibrium temperature is 23^ C . Heat gained by B equals heat lost by C : m s_B (23 - 19) = m s_C (28 - 23) 4 s_B = 5 s_C s_C = 4 5 s_B Let T be

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