Abathtub has 62.7 kg of water at 31.0 c. how much water at 76.0 c must be added to raise the temperature to 40.3 c?

m = mass of water in bathtub = 62.7 kg

= initial temperature of water in tub = 31 c

M = mass of water added = ?

= initial temperature of water added = 76 c

T = final equilibrium temperature of the system = 40.3 c

c = specific heat of water = 4186

Using conservation of heat

Heat gained by water in tub = Heat lost by water added

m c (T - ) = M c ( - T)

m (T - ) = M ( - T)

(62.7) (40.3 - 31) = M (76 - 40.3)

M = 16.3 kg