Question

Take 100 g of hot water at 80 °C in thermosflask. Add 200 g of cold water at 20 °C in the thermosflask.
Stir the contents and measure the temperature of the mixture. Then, the resultant temperature is
[No heat lost or gained]
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Answer 1

GIVEN -

Mass of hot water (m₁) = 100 g

Temperature of hot water (t₁) = 80°C

Mass of cold water (m₂) = 200 g

Temperature of cold water (t₂) = 20°C

ASSUMPTION -

No heat is lost or no heat is gained during the entire process

THEORY -

According to the principle of calorimetry, the amount of heat lost by the hot body is equal to the amount heat gained by the cold body for an insulated system.

TO FIND -

The final temperature of the mixture

CALCULATION -

                        Let the final temperature of the mixture be t

By principle of calorimetry,

m₁ X c₁ X (t₁-t) = m₂ X c₂ X (t-t₂)

Both the specific heat capacities cancel each other since both the hot and cold bodies are water and hence, they have equal specific heat capacities

= > m₁ X (t₁ - t) = m₂ X (t-t₂)

= > 100 X  (80 - t) = 200 X  (t -  20)

= > 80 - t = 2 (t - 20)

= > 80 - t = 2t - 40

= > 80 + 40 = 2t + t

= > 120 = 3t

= > t = 120/3

= >t = 40°C

ANSWER -

The final temperature of the mixture of 100g of hot water at 80°C and 200g of cold water at 20°C in the thermosflask is 40°C.