2 liters of water at 80.c is found into a plastic bucket containing 10 liters of water at 20.c what is the final temperature of water ( density of water 1kg/litre) (neglect the heat gained by bucket and specific heat capacity of water = 1cal/gm.c ?

The sum of the heats gained is zero.

2*(cw)(Tf-80)+10*cw(Tf-20)=0

Now, with the magic of algebra, solve for Tf. Notice that cw, the specific heat of water divides out, and it does not enter the calculation

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To find the final temperature of the water after mixing, we can use the principle of conservation of energy. The heat lost by the hot water will be equal to the heat gained by the cold water.

Let's calculate the heat lost by the hot water first.
Mass of hot water = volume x density = 2 liters x 1 kg/liter = 2 kg
Temperature change of hot water = final temperature - initial temperature = T - 80

Heat lost by hot water = mass x specific heat capacity x temperature change
Heat lost by hot water = 2 kg x 1 cal/gm.c x (T - 80)

Now, let's calculate the heat gained by the cold water.
Mass of cold water = volume x density = 10 liters x 1 kg/liter = 10 kg
Temperature change of cold water = final temperature - initial temperature = T - 20

Heat gained by cold water = mass x specific heat capacity x temperature change
Heat gained by cold water = 10 kg x 1 cal/gm.c x (T - 20)

Since the heat lost by the hot water is equal to the heat gained by the cold water, we can set up an equation:
2 kg x 1 cal/gm.c x (T - 80) = 10 kg x 1 cal/gm.c x (T - 20)

Now, let's solve for T, the final temperature:

2(T - 80) = 10(T - 20)
2T - 160 = 10T - 200
8T = 40
T = 5

Therefore, the final temperature of the water will be 5 degrees Celsius.