Question

A bathtub has 62.7 kg of water at 31.0

Answer 1

m = mass of water in bathtub = 62.7 kg

$T_{ti}$ = initial temperature of water in tub = 31 c

M = mass of water added = ?

$T_{ai}$ = 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 - $T_{ti}$) = M c ( $T_{ai}$ - T)

m (T - $T_{ti}$) = M ( $T_{ai}$ - T)

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

M = 16.3 kg