Three liquids $A,B\ and\ C$ of masses $400 gm,\ 600 gm\ and\ 800 gm$ are at $30^{0}C$, $40^{0}C$ and $50^{0}C$ respectively. When $A$ and $B$ are mixed, resultant temperature is $36^{0}C$ and when $B$ and $C$ are mixed, resultant temperature is $44^{0}C$. The ratio of their specific heats are :

Apply the principle of calorimetry, where mass times specific heat times temperature change is equal for both liquids during mixing. When mixing A and B, 400 * Sa * (36 - 30) = 600 * Sb * (40 - 36), which simplifies to 2400 * Sa = 2400 * Sb and shows that Sa equals Sb. When mixing B and C, 600 * Sb * (44 - 40) = 800 * Sc * (50 - 44), giving 2400 * Sb = 4800 * Sc, which means Sb equals 2 * Sc. Setting Sa = Sb = 2 * Sc, the ratio of their specific heats Sa : Sb : Sc is 2 : 2 : 1.

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