# A bucket contains 8 kg of water at 25°C and 2 kg of water at 80°C is poured into it. Neglecting the heat absorbed by the bucket, calculate the final temperature of water.

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By the principle of mixtures,

m x c (T1-T) = m x c x(T-T2)

2 x 4200(80-T) = 8 x 4200(T-25)

(4200 on both sides get cancelled)

160-2T = 8T-200

360 = 10T

T= 36 degree Celcius

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Let the final temperature be T

s be specific heat of water

amount of heat in bucket, hot water is equal to the final mixed water

8 *25 * s + 2 * 80 * s = (8+2) * s * T

T = 36 deg C

s be specific heat of water

amount of heat in bucket, hot water is equal to the final mixed water

8 *25 * s + 2 * 80 * s = (8+2) * s * T

T = 36 deg C