How much ice, initially at 0°C, is needed to cool 1.8 kg of tea from 80°C to 10°C?

To determine how much ice is needed to cool the tea, we first need to calculate the heat that must be removed from the tea to lower its temperature from 80°C to 10°C. The specific heat capacity of water is about 4.18 J/g°C.

1. Calculate the heat lost by the tea:

• Mass of tea = 1.8 kg = 1800 g

• Temperature change = 80°C - 10°C = 70°C

• Heat lost (Q) by the tea can be calculated as:

[

Q = mc\Delta T = (1800 , \text{g}) \times (4.18 , \text{J/g°C}) \times (70°C)

]

[

Q = 1800 \times 4.18 \times 70 = 525,240 , \text{J}

]

2. Since ice at 0°C needs to absorb the heat to melt and then gain the heat to reach 10°C (if we want the resultant mixture at that temperature), we consider the latent heat of fusion (approximately 334 J/g) to melt the ice,