Three liquids $A, B a n d C$ of masses $400 g m, 600 g m a n d 800 g m$ 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 :

2 : 1 : 1

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3 : 2 : 1

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2 : 2 : 1

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1 : 4 : 9

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Solution

The correct option is C $2 : 2 : 1$
When $A$ and $B$ are mixed,
$m_{1} . c_{1} . Δ T_{1} = m_{2} . c_{2} . Δ T_{2}$
$400 (c_{1}) (36 - 30) = 600 (c_{2}) (40 - 36)$
$\frac{c_{1}}{c_{2}} = 1$

When $B$ and $C$ are mixed
$600 (c_{2}) (44 - 40) = 800 (c_{3}) (50 - 44)$
$\frac{c_{2}}{c_{3}} = 2$
$∴ c_{1} = c_{2} = 2 c_{3}$
$c_{1} : c_{2} : c_{3} = 2 : 2 : 1$

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Three liquids A,B and C of masses 400gm, 600gm and 800gm are at 300C, 400C and 500C respectively. When A and B are mixed, resultant temperature is 360C and when B and C are mixed, resultant temperature is 440C. The ratio of their specific heats are :

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