A thermos bottle contains 250 g of coffee at 88 0C. You then decide to add 27 g of milk at 5 0C. What is the equilibrium temperature of the mixture? Assume no heat is loss to the thermos bottle and that the specific heat of water, coffee and milk is about the same.

Answer is 79.909 degrees C, but don't know how to get that

mc(Tf - Ti)coffee + mc(Tf - Ti)milk = 0

solve for Tf (and you'll need to look up the specific heat of water)

To find the equilibrium temperature of the mixture, we can use the principle of conservation of energy. According to this principle, the heat gained by the coffee and milk must equal the heat lost by the thermos bottle.

Let's denote the equilibrium temperature of the mixture as T°C.

First, we need to calculate the heat gained by the coffee (Qcoffee) and the heat gained by the milk (Qmilk).

The equation to calculate heat is given by:

Q = mcΔT

where Q is the heat gained or lost, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.

For the coffee:
m = 250 g
c = specific heat capacity (assumed to be the same as water) = 4.18 J/g°C (this is the value commonly used)
ΔT = T - 88°C

So, Qcoffee = (250 g)(4.18 J/g°C)(T - 88°C)

For the milk:
m = 27 g
c = specific heat capacity (assumed to be the same as water) = 4.18 J/g°C
ΔT = T - 5°C

So, Qmilk = (27 g)(4.18 J/g°C)(T - 5°C)

Now, according to the principle of conservation of energy, the total heat gained by the coffee and milk must equal the heat lost by the thermos bottle.

Since no heat is lost to the thermos bottle, the total heat gained by the coffee and milk is equal to zero. Therefore:

Qcoffee + Qmilk = 0
(250 g)(4.18 J/g°C)(T - 88°C) + (27 g)(4.18 J/g°C)(T - 5°C) = 0

Now, we can solve this equation to find the equilibrium temperature (T).

(250 g)(4.18 J/g°C)(T - 88°C) + (27 g)(4.18 J/g°C)(T - 5°C) = 0
(1045 J/°C)(T - 88°C) + (112.86 J/°C)(T - 5°C) = 0
1045T - 91960 + 112.86T - 564.3 = 0
1157.86T - 92524.3 = 0
1157.86T = 92524.3
T ≈ 79.91°C

Therefore, the equilibrium temperature of the mixture is approximately 79.91°C.