A container holds 3kg of water at 25 degree celcius. If 0.5kg of iron at 80 degree celcius is added to the water in the contain. What is the?

(i) final temperature of the container.
(ii) Quantity of heat gained by water

To find the final temperature of the container, we can apply the principle of heat transfer, which states that heat lost is equal to heat gained.

First, let's calculate the heat lost by the iron:

Heat lost by iron = m * c * ΔT

where
m = mass of the iron = 0.5 kg
c = specific heat capacity of iron (assumed to be 0.45 J/g°C)
ΔT = change in temperature = final temperature - initial temperature = final temperature - 80°C (since the initial temperature of the iron is 80°C)

Heat lost by iron = 0.5 kg * 0.45 J/g°C * (final temperature - 80°C)

Now, let's calculate the heat gained by the water:

Heat gained by water = m * c * ΔT

where
m = mass of the water = 3 kg
c = specific heat capacity of water (taken as 4.18 J/g°C)
ΔT = change in temperature = final temperature - initial temperature = final temperature - 25°C (since the initial temperature of the water is 25°C)

Heat gained by water = 3 kg * 4.18 J/g°C * (final temperature - 25°C)

Since the heat lost by the iron is equal to the heat gained by the water, we can set up an equation:

0.5 kg * 0.45 J/g°C * (final temperature - 80°C) = 3 kg * 4.18 J/g°C * (final temperature - 25°C)

Simplifying and solving for final temperature:

0.225 (final temperature - 80) = 12.54 (final temperature - 25)
0.225 final temperature - 18 = 12.54 final temperature - 313.5
0.225 final temperature - 12.54 final temperature = -313.5 + 18
-12.315 final temperature = -295.5
final temperature = -295.5 / -12.315
final temperature ≈ 24°C

So, the final temperature of the container is approximately 24°C.

To find the quantity of heat gained by the water, we can substitute the final temperature into the heat gained by water equation:

Heat gained by water = 3 kg * 4.18 J/g°C * (24°C - 25°C)
Heat gained by water = -12.54 J

Therefore, the quantity of heat gained by the water is approximately -12.54 J.