The temperature of equal masses of three different liquids A, B and C are ${12}^{\circ }\text{C}$ ,  ${19}^{\circ }\text{C}$ and ${28}^{\circ }\text{C}$  respectively, the temperature when A and B are mixed is  ${16}^{\circ }\text{C}$, when B and C are mixed is ${23}^{\circ }\text{C}$ , what is the temperature when A and C are mixed?

detailed solution

Correct option is C

Case 1: When A and B mixed Resultant= 16ocapply principle of method of mixtures, heat lost by hot body B= heat gained by cold body Aheat lost or gain = MS(temperature difference),where M is mass of the body , S is specific heat of the bodyheat gain by A= heat lost by B,  here common temperature is 160C MS1[16-12]=MS2[19-16]S2=43S1----(1)Case 2: When B and C mixedheat gain by B = heat lost by C. here common temperature is 23 CMS2[23-19]=MS3=[28-23]4S2=5S3substitute equation (1)4×43S1=5S3S3=1615S1----(2)Case 3: When A and C are mixedheat gain by A = heat lost by CMS1[T-12]=MS3[28-T]substitute equation (2) S1[T-12]=1615S1[28-T]T=20.26octhis is the temperature when A and C are mixed