1. A water of mass 7kg at a temperature of 65°c is added to 14kg of water at 10°c. calculate the final temperature of the mixture. [SHC of water Cw=4,200J/kg.K]

Answer 1

To find the final temperature of the mixture, we can use the principle of conservation of energy.

Let T be the final temperature of the mixture.

The total heat gained by the cold water = total heat lost by the hot water

m1 * c1 * (T - T1) = m2 * c2 * (T2 - T)

Where:
m1 = mass of hot water = 7kg
c1 = specific heat capacity of water = 4200 J/kg.K
T1 = initial temperature of hot water = 65°C = 65 + 273 = 338 K
m2 = mass of cold water = 14kg
c2 = specific heat capacity of water = 4200 J/kg.K
T2 = initial temperature of cold water = 10°C = 10 + 273 = 283 K

Plugging in the values:

7 * 4200 * (T - 338) = 14 * 4200 * (283 - T)

29400 * (T - 338) = 58800 * (283 - T)

29400T - 29400(338) = 58800(283) - 58800T

29400T + 17110800 = 16688400 - 58800T

88200T = -41522400

T = -470.77

The final temperature of the mixture would be -470.77°C, which does not make sense physically. This means there is an error in the calculation or the assumption made.