Three containers `C_1, C_2` and `C_3` have water at different temperatures. The table below shows the final temperature T when different amounts of water (given in litres) are taken from each containers and mixed (assume no loss of heat during the process)

The value of (in °C to the nearest integer) is …….

Answer

50

Explanation

According to table and applying law of calorimetry
`2T_1 +2T_2 = (2+2) 45^@" (1)`
`3T_2 +1T_3 =(3+1)65^@" (2)"`
`T_1 +3T_3 =(1+3)67.5^@" (3)"`
Solving `T_1 =30^@, T_2 = 60^@, T_3 = 80^@`
Hence, `2T_1 +T_2+T_3=(3+1+1)theta," "200 = 4 theta," "theta = 50^@C`