Question

what would be the final temperature of a mixture of 50 gm of water at 20 degree celsius temperature and 50g of water at 40 degree celsius temperature?

Answer 1

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 =

⇒ 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.