Answer:
The rock has a mass of 4.02 kg
Explanation:
<u>Step 1: </u>Data given
Mass of the rock = TO BE DETERMINED
Temperature of the rock = 500 °C
Mass of the water =4.24 kg
⇒ loses 0.044kg as vapor
Initial temperature of the water = 29°C
Final temperature = 100°C
Specific heat of rock = 0.20 kcal/kg °C
Specific heat of water = 1kcal/kg°C
Latent heat of vaporization = 539 kcal/kg
<u>Step 2:</u> formules
Qlost,rock + Qgained,water = 0
Qtotal,water = Qwater +Qvapor
<u>Step 3: </u>Calculate Qvapor
Qvapor = mass of vapor * Latent heat of vapor
Qvapor = 0.044kg * 539 kcal/kg = 23.716 kcal
<u>Step 4: </u>Calculate Qwater
Qwater = mass of water * specific heat * Δtemperature
Qwater = 4.196 kg * 1kcal/kg°C *( 100-29)
Qwater = 297.916 kcal
<u>Step 5:</u> Calculate Qwater,total
Qwater,total = Qwater + Qvapor
Qwater,total = 23.716 kcal + 297.916 = 321.632 kcal
<u>Step 6</u>: Calculate Qrock
Qrock = mass of rock * specific heat rock * Δtemperature
Qrock = mass of rock * 0.20 kcal/kg°C * (100-500)
Qrock = mass of rock * -80 kcal/kg
<u>Step 7:</u> Calculate mass of rock
Qlost,rock + Qgained,water = 0
Qlost,rock = -Qgained,water
mass of rock * -80 kcal/kg = -321.632 kcal
mass of rock = 4.02 kg
The rock has a mass of 4.02 kg
