A thermos contains 147 cm3 of coffee at 95.0 °C. To cool the coffee, you drop two 12.4-g ice cubes into the thermos. The ice cubes are initially at 0 °C and melt completely. What is the final temperature of the coffee in degrees Celsius? Treat the coffee as if it were water.

C is specific heat of water

grams of coffee assumed the same as cm^3 of coffee
24.8 *[heat of fusion of water + C (T-0)] = 147 * C * (95-T)

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To find the final temperature of the coffee, we can use the principle of conservation of energy. We'll need to calculate the amount of heat lost by the coffee when it cools and the amount of heat gained by the ice when it melts.

First, let's calculate the heat lost by the coffee. We can use the equation:

Q = mcΔT

Where:
Q = heat lost or gained
m = mass
c = specific heat capacity
ΔT = change in temperature

The specific heat capacity, c, for water is approximately 4.18 J/g°C.

The mass of the coffee can be calculated using the density of water, which is 1 g/cm³:

Mass = Volume x Density
Mass = 147 cm³ x 1 g/cm³
Mass = 147 g

ΔT = final temperature - initial temperature = Tfinal - 95.0 °C

Now we can calculate the heat lost by the coffee:

Qcoffee = mcoffee x cwater x ΔT

Qcoffee = 147 g x 4.18 J/g°C x (Tfinal - 95.0 °C)

Next, let's calculate the heat gained by the ice. The heat gained by the ice can be calculated using the equation:

Qice = mice x Hf

Where:
mice = mass of ice
Hf = heat of fusion, which is the amount of heat required to melt 1 g of ice, and for water, it is 334 J/g.

The mass of each ice cube is given as 12.4 g. Therefore, for two ice cubes, the total mass of ice is:

mice = 2 x 12.4 g = 24.8 g

Qice = 24.8 g x 334 J/g

According to the principle of conservation of energy, the heat lost by the coffee is equal to the heat gained by the ice. Thus:

Qcoffee = Qice

147 g x 4.18 J/g°C x (Tfinal - 95.0 °C) = 24.8 g x 334 J/g

Now we can solve for the final temperature, Tfinal:

147 g x 4.18 J/g°C x (Tfinal - 95.0 °C) = 24.8 g x 334 J/g

Simplifying the equation:
614.46(Tfinal - 95) = 8267.2

Now, solve for Tfinal:
614.46(Tfinal - 95) = 8267.2
614.46Tfinal - 614.46(95) = 8267.2
614.46Tfinal - 58473.7 = 8267.2
614.46Tfinal = 66740.9
Tfinal = 108.6

Therefore, the final temperature of the coffee is approximately 108.6 °C.