Conservation of Heat  

This model should approximate a Specific Heat experiment where a sample of hot metal is placed in cool water and the system is allowed to come to thermal equilibrium. Some of the constants here are measured values for the metal samples used in our experiment. This is one of the few models which students do not build.

THE MODEL
Vensim Version STELLA Version

[Diagram Level | Equations Level | Graphs ]



Metal_heat(t) = Metal_heat(t - dt) + 
     (heat_transferred_from_water_to_metal - heat_transferred_from_metal_to_water)
     * dt
INIT Metal_heat = mass_of_metal*specific_heat_of_metal*init_temp_of_metal

heat_transferred_from_water_to_metal =
     water_thermal_conductivity*surface_area*(Water_temp-Metal_temp)/length_water

heat_transferred_from_metal_to_water =
     water_thermal_conductivity*surface_area*(Metal_temp-Water_temp)/length_metal

Water_heat(t) = Water_heat(t - dt) + (heat_transferred_from_metal_to_water
     - heat_transferred_from_water_to_metal) * dt
INIT Water_heat = mass_of_water*specific_heat_of_water*init_temp_of_water

heat_transferred_from_metal_to_water =
     water_thermal_conductivity*surface_area*(Metal_temp-Water_temp)/length_metal

heat_transferred_from_water_to_metal =
     water_thermal_conductivity*surface_area*(Water_temp-Metal_temp)/length_water

length_metal = .01
length_water = .04
surface_area = .0044

water_thermal_conductivity = GRAPH(Water_heat)
     (0.00, 0.561), (10.0, 0.58), (20.0, 0.598), (30.0, 0.615), (40.0, 0.63),
     (50.0, 0.643), (60.0, 0.654), (70.0, 0.663), (80.0, 0.67), (90.0, 0.675),
     (100, 0.679)

Metal_temp(t) = Metal_temp(t - dt) + (- change_in_metal_temp) * dt
INIT Metal_temp = init_temp_of_metal

change_in_metal_temp =
     (heat_transferred_from_metal_to_water-heat_transferred_from_water_to_metal)/
     (mass_of_metal*specific_heat_of_metal)

Water_temp(t) = Water_temp(t - dt) + (change_on_water_temp) * dt
INIT Water_temp = init_temp_of_water

change_on_water_temp =
     (heat_transferred_from_metal_to_water-heat_transferred_from_water_to_metal)/
     (mass_of_water*specific_heat_of_water)

final_temp =
     (mass_of_metal*specific_heat_of_metal*init_temp_of_metal+mass_of_water*
     specific_heat_of_water*init_temp_of_water)/
     (mass_of_water*specific_heat_of_water+mass_of_metal*specific_heat_of_metal)

init_temp_of_metal = 100
init_temp_of_water = 20
mass_of_metal = .2
mass_of_water = .5
specific_heat_of_metal = .907
specific_heat_of_water = 4.18
 
Time Specs
Range: 0 - 3 , dT = 0.02 , Integration Method = Runge-Kutta 4




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