A copper of mass 400g is heated until it's temperature becomes 250degree celcius. It is dropped into water weighing 200g at 50 degree celcius.calculate the mass of water vapour produced.
figure the heat in the copper. when dropped in water, it will make steam until it(the copper) is 100C.
heat copper loses : 400*ccu*(100-250)
amount of steam: that heat above (400*Ccu*(150))=masssteam(hvaporwater)
solve for mass steam.
To calculate the mass of water vapor produced, we need to use the concept of heat transfer. The heat lost by the hot copper will be gained by the water, resulting in a temperature change and eventually the evaporation of some water into vapor.
First, let's determine the initial and final thermal energies of the copper and the water. We can use the specific heat capacity and the equation:
Q = mcΔT,
where Q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the temperature change.
For the copper:
Initial thermal energy = mcΔT
= (0.4 kg) × (0.385 J/g·°C) × (250°C - 50°C)
= 0.4 kg × 200 g/°C × 200°C
= 16,000 J or 16 kJ.
Since the heat lost by the copper is gained by the water, we have:
Heat gained by water = Heat lost by copper.
For the water:
Final temperature of water = Final temperature of mixture = 100°C (assuming a final thermal equilibrium temperature).
Initial thermal energy of water = mcΔT
= (0.2 kg) × (4.186 J/g·°C) × (100°C - 50°C)
= 0.2 kg × 4,186 J/kg·°C × 50°C
= 41,860 J or 41.86 kJ.
Since the heat lost by the copper equals the heat gained by the water, the total heat transferred is:
Total heat transferred = Heat lost by copper = Heat gained by water
= 16 kJ.
Now, to calculate the mass of water vapor produced, we need to consider the heat of vaporization. The heat of vaporization of water is 2.26 kJ/g.
Mass of water vapor produced = (Total heat transferred) / (Heat of vaporization of water)
= 16 kJ / 2.26 kJ/g
≈ 7.08 g.
Therefore, the mass of water vapor produced is approximately 7.08 grams.