there are 3 liquids a,b,c of equal masses,they are at temprature10,15,25centigrade.when liquid a and b are mixed together common temprature is 12centigrade when b and c are mixed then common temprature is21centigrade.what will be the common temprature of a and c.

Hi

Use principle of calorimetry

For A and B

m s_a (12 - 10) = m s_b (15 - 12)

=> s_a / s_b = 3/2   ---------------------------------(1)

For B and C

m s_b (21 - 15) = m s_c (25 - 21)

=> s_b / s_c = 4/6 = 2/3 --------------------------------(2)

From (1) and (2)

s_a / s_c = 3/2*2/3 = 1  -----------(3)

Now when A and C mixed let final temp = T

m s_a (T - 10) = m s_c (25 - T)                          [from(3)]

=> T =35/2 = 17.5 ⁰C

Thanks

Anurag Kishore