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Physics-

General

Easy

Question

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

4:3
3:4
2:3
3:2

The correct answer is: 2:3

Given that T_A = 30°c
T_B = 20°c
equilibrium temperature after mixing is (T) = 26°c
temperature lost by body A,
$capital delta T subscript A end subscript equals T subscript A end subscript minus T equals 30 minus 26 equals 4 to the power of ring operator end exponent C$
temperature gained by body B,
$capital delta T subscript B end subscript equals T minus T subscript B end subscript equals 26 minus 20 equals 6 to the power of ring operator end exponent C$
we know that
$Q subscript A end subscript equals m subscript A end subscript S subscript A end subscript capital delta T subscript A end subscript$
$Q subscript B end subscript equals m subscript B end subscript S subscript B end subscript capital delta T subscript B end subscript$
$Q subscript A end subscript equals Q subscript B end subscript$ B (principle of calorimetry)
$m subscript A end subscript S subscript A end subscript capital delta T subscript A end subscript equals m subscript B end subscript S subscript B end subscript capital delta T subscript B end subscript$
$open parentheses m subscript A end subscript equals m subscript B end subscript equals m close parentheses$
$m S subscript A end subscript capital delta T subscript A end subscript equals m S subscript B end subscript capital delta T subscript B end subscript$
$rightwards double arrow fraction numerator S subscript A end subscript over denominator S subscript B end subscript end fraction equals fraction numerator capital delta T subscript B end subscript over denominator capital delta T subscript A end subscript end fraction$
$rightwards double arrow fraction numerator S subscript A end subscript over denominator S subscript B end subscript end fraction equals fraction numerator 6 over denominator 4 end fraction$
$therefore S subscript A end subscript equals S subscript B end subscript equals 3 colon 2$

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