Questions

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?

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a

28∘c

b

31∘c

c

20.26∘c

d

19.5∘c

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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

Similar Questions

A bullet of mass 5g , Travelling with a speed of 210 m/s , strikes a fixed wooden target . One half its kinetic energy is converted in to heat in the bullet while the other half is converted in to heat in the wood. The rise of temperature of the bullet if the specific heat of the material is 0.030 cal/$\left({\text{g-}}^{\text{0}}\text{C}\right)\left(1cal=4.2\times {10}^{7}\text{ergs}\right)$ close to:

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