First slide

Calorimetry

Question

The temperature of equal masses of three different liquids A, B and C are 12^oC, 19^oC and 28^oC respectively. The temperature when A and B are mixed is 16^oC and when B and C are mixed is 23^oC. The temperature when A and C are mixed is

Moderate

A

${18.2}^{\circ} C$
B

$22^{\circ} C$
C

${20.2}^{\circ} C$
D

${25.2}^{\circ} C$

Solution

Heat gain = heat lost
$\begin{array}{l} C_{A} (16 - 12) = C_{B} (19 - 16) \Rightarrow \frac{C_{A}}{C_{C}} = \frac{15}{16} = \frac{5}{4} \\ and C_{B} (23 - 19) = C_{C} (28 - 23) \Rightarrow \frac{C_{A}}{C_{C}} = \frac{5}{4} \\ \Rightarrow \frac{C_{A}}{C_{C}} = \frac{15}{16} . . . . . . . . . . . . . (i) \end{array}$
If $θ$ is the temperature when A and C are mixed then,
$C_{A} (θ - 12) = C_{C} (28 - θ) \Rightarrow \frac{C_{A}}{C_{C}} = \frac{28 - θ}{θ - 12}$ …………(ii)
On solving equation (i) and (ii), $θ = 20 {.2}^{\circ} C .$

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