The final temperature of a mixture of 100g of water at 20°C and 50g of water at 50°C is 30°C.
The amount of heat lost by the hotter sample = The amount of heat gained by the cooler water sample
The amount of heat gained by the cooler water sample is: -
Q1₁= m₁c(T – T₁)
The amount of heat lost by the hotter water sample is: -
Q₂ = m₂c(T₂ - T)
Q₁ = Q₂
m₁c(T – T₁) = m₂c(T₂ - T)
T = (m₁T₁ + m₂T₂)/(m₁+ m₂)
Let the final temperature of the mixture of 100g of water at 20°C and 50g of water at 50°C be T.
m₁ = 100g
T₁ = 20°C
m₂ = 50g
T₂ = 50°C
The final temperature of water = (100*20+50*50)/(100+50)
= (2000+2500)/(150)
=4500/150
=30°C
Therefore , the final temperature of a mixture of 100g of water at 20°C and 50g of water at 50°C is 30°C.
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