Two liquids A and B are at 30ºC and 20ºC. When mixed in equal masses the temperature of the mixture is found to be 26ºC. The ratio of specific heats of A and B is

Engineering

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Thermodynamics

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Question

Two liquids A and B are at 30ºC and 20ºC. When mixed in equal masses the temperature of the mixture is found to be 26ºC. The ratio of specific heats of A and B is

1 : 1

4 : 3

2 : 3

3 : 2

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When two liquids of equal mass mix, heat lost by hotter liquid equals heat gained by colder liquid. Let specific heats be c_A and c_B.

Heat lost by A: m c_A (30 - 26) = 4 m c_A

Heat gained by B: m c_B (26 - 20) = 6 m c_B

Set equal: $4 c_{A} = 6 c_{B}$

Thus, $\frac{c_{A}}{c_{B}} = \frac{6}{4} = \frac{3}{2}$

Final Answer: 3 : 2