What would be the final temperature of a mixture of 50g of water at 20°C temperature and 50g of water at 40°C temperature? (AS1)

Question

Philoid · Accepted Answer

Let the final temperature of the mixture of 50g of water at 20°C temperature and 50g of water at 40°C be T.

For the first solution i.e mixture of 50g of water at 20°C temperature: -

Let the mass of water be m₁ = 50g

Let the temperature of water be = T₁ = 20°C

Similarly, For the second solution i.e mixture of 50g of water at 40°C temperature: -

Let the mass of water be m₂ = 50g

Let the temperature of water be = T₂ = 40°C

Let the specific heat capacity of water be S.

The amount of heat gained by the cooler water sample is: -

Q₁ = m₁S(T – T₁)

The amount of heat lost by the hotter water sample is: -

Q₂ = m₂S(T₂ - T)

According to the principle of method of mixtures we know that: -

The amount of heat lost by the hotter sample = The amount of heat gained by the cooler water sample

∴ Q₁ = Q₂

⇒ T =

⇒ T = 30°C

Hence, the final temperature of a mixture of 50g of water at 20°C temperature and 50g of water at 40°C temperature would be 30°C.