The Temperatures of Equal Masses of Three Different Liquids A, B and C Are 12°C, 19°C and 28°C Respectively. the Temperature When a and B Are Mixed is 16°C, and When B and C Are Mixed, It is 23°C. - Physics

Sum

The temperatures of equal masses of three different liquids A, B and C are 12°C, 19°C and 28°C respectively. The temperature when A and B are mixed is 16°C, and when B and C are mixed, it is 23°C. What will be the temperature when A and C are mixed?

Solution

Given:
Temperature of A = 12°C
Temperature of B = 19°C
Temperature of C = 28°C
Temperature of mixture of A and B = 16°C
Temperature of mixture of B and C = 23°C

Let the mass of the mixtures be and the specific heat capacities of the liquids A, B and C be CACB, and CC, respectively.

According to the principle of calorimetry, when A and B are mixed, we get

Heat gained by Liquid A = Heat lost by liquid B
⇒ MCA (16 − 12) = MCB (19 − 16)
⇒ 4MCA = 3 MCB

rArrMC_A=(3/4)MC_B............(1)

When B and C are mixed:
Heat gained by liquid B = Heat lost by liquid C
MCB (23 − 19) = MCC (28 − 23)
⇒ 4MCB = 5 MCC

rArr M_(C C)=(4/5)M_(C B).............(2)

When A and C are mixed:
Let the temperature of the mixture be T. Then,
Heat gained by liquid A = Heat lost by liquid C
⇒ MCA (T − 12) = MCC (28 − T)

Using the values of MCand MCC, we get

rArr(3/4)MC_B(T-12)=(4/5)MC_B(28-T)  ............["From eq. (1) and (2)"]

rArr(3/4)(T-12)=(4/5)(28-T)

(3×5) (T12) = (4×4) (28T)

15T180 = 44816T

31T = 628

rArrT=628/31=20.253^oC

T = 20.3°C

Concept: Measurement of Temperature
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HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 3 Calorimetry
Q 3 | Page 47
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