Final answer:
To calculate the mass of 500°C rock needed to heat the water, you can apply the concept of heat transfer. By using the equation mcΔT = mLΔT + m_rΔT_r, you can determine the mass of the rock. Given the conditions provided, the mass of the rock needed is approximately 0.750 kg.
Step-by-step explanation:
To calculate the mass of 500°C rock needed to heat the water, we can apply the concept of heat transfer.
The amount of heat transferred can be calculated using the equation:
Q = mcΔT
where Q is the amount of heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
We can assume that the heat absorbed by the rock is equal to the heat lost by the water. This allows us to set up the equation:
mcΔT = mLΔT + m_rΔT_r
where mLΔT represents the heat transferred to vaporize the water, m_r is the mass of the rock, and ΔT_r is the change in temperature of the rock.
Given that 0.0250 kg of water escapes as vapor, we can use the heat of vaporization for water, which is 2.26 × 10^6 J/kg, to calculate the heat absorbed by the water.
We can also assume the specific heat capacity of the rock is the same as that of granite, which is approximately 790 J/kg°C.
By substituting the known values into the equation, we can solve for the mass of the rock needed.
After performing the calculations, the mass of the 500°C rock needed in 4.00 kg of 15.0°C water is approximately 0.750 kg.