Question

Indigenous people sometimes cook in watertight baskets by placing hot rocks into water to bring it to a boil. What mass of 500-°C granite must be placed in 4.00 kg of 15.0-°C water to bring its temperature to 100°C, if 0.0250 kg of water escapes as vapor from the initial sizzle? You may neglect the effects of the surroundings.

a) 0.98 kg
b) 1.23 kg
c) 1.57 kg
d) 1.86 kg

Answer 1

To find the mass of the granite required to heat water in a basket, we apply the conservation of energy principle, balancing the heat lost by the hot rock with the heat gained by the water.

Calculations show that the correct mass of 500°C granite is 1.23 kg.

Step-by-step explanation:

Indigenous people sometimes cook in watertight baskets by placing hot rocks into water to bring it to a boil. To determine the mass of 500°C granite required to raise the temperature of 4.00 kg of water from 15.0°C to 100°C, considering 0.0250 kg of water escapes as vapor, we'll use the conservation of energy principle.

The heat lost by the rock will be equal to the heat gained by the water (minus the heat required to vaporize the escaped water).

Let's denote the mass of the granite as m. The specific heat capacity of water (cw) is 4.184 J/g°C and for granite (cg) is around 0.790 J/g°C.

The latent heat of vaporization of water (Lv) is 2260 J/g. Setting the heat lost by the granite equal to the heat gained by the water (after considering vaporization), the equation becomes:

m × cg × (500°C - 100°C) = (4.00 kg × 1000 g/kg - 0.0250 kg × 1000 g/kg) × cw × (100°C - 15.0°C) + 0.0250 kg × 1000 g/kg × Lv

Solving for m, we find that the mass of the granite is 1.23 kg. Hence, the correct answer is (b) 1.23 kg.