How to Cool Freshly Brewed Tea Without Watering It Down Too Much

What is the minimum amount of ice needed to cool 2.36 kg of freshly brewed tea at 93.30°C to 12.19°C without watering it down too much?

1. 0.5 kg

2. 1 kg

3. 2 kg

Answer

The minimum amount of ice needed to cool 2.36 kg of freshly brewed tea from 93.30°C to 12.19°C without watering it down too much is 1 kg.

To cool the freshly brewed tea without watering it down too much, you need to remove the heat from the tea. This can be done by calculating the heat required to cool the tea from its initial temperature to the desired temperature.

Explanation:

To cool the freshly brewed tea from 93.30°C to 12.19°C without watering it down too much, we need to calculate the amount of heat that needs to be removed from the tea. First, we calculate the heat required to cool the tea from 93.30°C to 0°C using the specific heat of water. Then, we calculate the heat required to cool the tea from 0°C to 12.19°C using the latent heat of fusion for ice. Finally, we calculate the mass of ice needed using the given information about its initial temperature.

Using the formula Q = mcΔT, where Q is the heat, m is the mass, and ΔT is the change in temperature, the heat required to cool the tea from 93.30°C to 0°C would be Q = (2.36 kg)(4190 J/kg/K)(93.30°C - 0°C). The heat required to cool the tea from 0°C to 12.19°C would be Q = (2.36 kg)(3.34 x 10^5 J/kg) + (2.36 kg)(2010 J/kg/K)(12.19°C - 0°C).

To calculate the mass of ice needed, we use the formula Q = mL, where Q is the heat, m is the mass, and L is the latent heat of fusion for ice. Rearranging the formula, we have m = Q/L. Plugging in the values, we get m = (3.34 x 10^5 J)/(3.34 x 10^5 J/kg) = 1 kg. Therefore, the minimum amount of ice needed is 1 kg.