Question

One litre of water at 40˚C is mixed with one litre of water at 60˚C. The

temperature of the mixture will be (choose the correct option and give reason

to support your answer). (i) 85˚C (ii) more than 60˚C but less than 85˚C (iii)

between 40˚C and 60˚C.​

Answer 1

Given : One litre of water at 40˚C is mixed with one litre of water at 60˚C

To Find : The temperature of the mixture will be

(i) 85˚C

(ii) more than 60˚C but less than 85˚C

(iii) between 40˚C and 60˚C.​

Solution:

Heat flows from an object at higher temperature to an object at lower temperature.

One litre of water at 40˚C is mixed with one litre of water at 60˚C

Volume of both are same

Heat will transfer from higher temperature water to lower temperature water

means from  60°C to 40°C

Hence 60°C temperature will decrease because of heat transferred to 40°C

and 40°C temperature will increase

Hence Temperature will be between 40˚C and 60˚C

One litre of water at 40˚C is mixed with one litre of water at 60˚C. The

temperature of the mixture will be between 40˚C and 60˚C.​

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Answer 2

Given:

One litre of water at 40˚C is mixed with one litre of water at 60˚C.

To find:

What will be the temperature of mixture?

Solution:

Theoritical Reasoning:

• When the hot water (at 60°C) is being put into the cold water (at 40°C), the heat from hot water is being used up to increase the temperature of the cold water. In turn, the temperature of hot water falls.

• Hence the temperature of the mixture becomes the equilibrium temperature between the upper and lower limit of the components (i.e. between 40°C and 60°C).

Calorimetric Calculation:

Let the mixture temperature be T:

Mass of water used = 1 L × 1000kg/m³ = 1 kg.

Specific heat capacity of water = 1 Cal/kg°C

Applying Law of Calorimetry:

$\therefore \: (m1)(c1)(\Delta T_{1}) = (m1)(c1)(\Delta T_{2})$

$\implies\: (1)(1)( {60}^{ \circ} - T) = (1)(1)(T - {40}^{ \circ} )$

$\implies\: {60}^{ \circ} - T = T - {40}^{ \circ}$

$\implies\: 2T = {100}^{ \circ}$

$\implies\: T = {50}^{ \circ}$

So, temperature of mixture is 50°C.

NOTE:

• If you are from class 11-12 , then you need to show the 2nd part of the answer (i.e. the calculations part) along with explaination.