Indigenous people sometimes cook in watertight baskets by placing
hot rocks into water to bring it to a boil. What mass of 500ºC rock must
be placed in 4.00 kg of 15.0ºC water to bring its temperature to 100ºC
, if 0.0250 kg of water escapes as vapor from the initial sizzle? You may
neglect the effects of the surroundings and take the average specific heat
of the rocks to be that of granite.
To solve this problem, we need to use the principle of heat transfer, specifically the equation for heat gained or lost through a temperature change:
Q = mcΔT,
where Q is the heat gained or lost, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
First, let's calculate the heat lost by the hot rocks. The initial temperature of the rocks is 500ºC, and we want to bring the water to 100ºC. Therefore, the change in temperature for the rocks is:
ΔT = 100ºC - 500ºC = -400ºC.
Next, we need to calculate the mass of water remaining after 0.0250 kg escapes as vapor. The initial mass of water is 4.00 kg, so the remaining mass is:
m_water = 4.00 kg - 0.0250 kg = 3.975 kg.
Now we can calculate the heat gained by the water. The specific heat capacity of water is 4186 J/kg·ºC. The change in temperature for the water is:
ΔT = 100ºC - 15ºC = 85ºC.
Let's calculate the heat gained by the water:
Q_water = mcΔT
= (3.975 kg) * (4186 J/kg·ºC) * (85ºC).
Finally, to bring the system into thermal equilibrium, the heat lost by the rocks (Q_rock) will equal the heat gained by the water (Q_water). Therefore, we can set up the following equation:
Q_water = Q_rock.
Substituting the expressions for Q_water and Q_rock, we have:
(3.975 kg) * (4186 J/kg·ºC) * (85ºC) = (m_rock) * (specific heat capacity of granite) * (-400ºC).
Now we can solve for the mass of the rock (m_rock):
m_rock = [(3.975 kg) * (4186 J/kg·ºC) * (85ºC)] / [(specific heat capacity of granite) * (-400ºC)].
Note that we need the specific heat capacity of granite to complete the calculation. Unfortunately, the specific heat capacity of granite is not provided in the question. You may need to refer to a reliable source or consult an appropriate reference material to obtain the specific heat capacity of granite.