Answer:
Need approximately 518.54 grams of ice cubes at -10°C to add to 1.0L of hot tea at 85°C to achieve a final temperature of 20°C.
Step-by-step explanation:
To calculate the number of grams of ice cubes required to reach the final temperature, we can use the principle of energy conservation. The energy lost by the hot tea will be equal to the energy gained by the ice cubes, which results in the final temperature.
The specific heat capacity of water is approximately 4.18 J/g°C, which means it takes 4.18 Joules of energy to raise the temperature of 1 gram of water by 1 degree Celsius.
Step 1: Calculate the energy lost by the hot tea.
The hot tea's initial temperature is 85°C, and its final temperature is 20°C.
Energy lost by hot tea = mass_hot_tea * specific_heat_water * (initial_temp_hot_tea - final_temp_mixture)
Given that 1.0L of hot tea is equal to 1000 grams (since the density of water is approximately 1 g/mL):
Energy lost by hot tea = 1000g * 4.18 J/g°C * (85°C - 20°C)
Step 2: Calculate the energy gained by the ice cubes.
The initial temperature of the ice cubes is -10°C, and the final temperature is 20°C.
Energy gained by ice cubes = mass_ice * specific_heat_water * (final_temp_mixture - initial_temp_ice)
Step 3: Equate the energy lost by the hot tea and the energy gained by the ice cubes.
1000g * 4.18 J/g°C * (85°C - 20°C) = mass_ice * 4.18 J/g°C * (20°C - (-10°C))
Step 4: Solve for the mass of the ice cubes (mass_ice):
1000g * 4.18 J/g°C * 65°C = mass_ice * 4.18 J/g°C * 30°C
mass_ice = (1000g * 4.18 J/g°C * 65°C) / (4.18 J/g°C * 30°C)
mass_ice = 65000g / 125.4
mass_ice ≈ 518.54g
Therefore, you need approximately 518.54 grams of ice cubes at -10°C to add to 1.0L of hot tea at 85°C to achieve a final temperature of 20°C.