A child has a fever. The temperature of his body is recorded as 103 degree farenheit by a thermometer . A doctor advised his mother to give medicine to lower the temperature. As we know evaporation causes cooling. The medicine given to child enhanced the evapouration. Calculate the rate of evaporation by this medicine if the temperature of the body of the child falls to 99 degree F in 25 min. Mass of child is 20kg,specific heat of human body is 4.2J/g/deg C and latent heat of vaporization is 2436J/g.
To calculate the rate of evaporation caused by the medicine, we need to consider the energy transfer involved in the process.
1. First, let's convert the temperature change from Fahrenheit to Celsius:
Initial temperature (T1) = 103°F = (103-32) × 5/9 = 39.4°C
Final temperature (T2) = 99°F = (99-32) × 5/9 = 37.2°C
2. Calculate the energy required to decrease the child's body temperature:
Energy = mass × specific heat × temperature change
= 20 kg × 4.2 J/g/°C × (T1 - T2)
= 20,976 J
3. Since we know that the medicine enhances evaporation, the change in energy is due to the heat absorbed for vaporization:
Change in energy = mass of water evaporated × latent heat of vaporization
4. Rearranging the equation, we can calculate the mass of water evaporated:
Mass of water evaporated = Change in energy / latent heat of vaporization
= 20,976 J / 2436 J/g
≈ 8.61 g
5. Finally, to find the rate of evaporation over 25 minutes, we divide the mass of water evaporated by the time:
Rate of evaporation = Mass of water evaporated / Time
= 8.61 g / (25 min × 60 s/min)
≈ 0.0057 g/s
Therefore, the rate of evaporation caused by the medicine is approximately 0.0057 grams per second.
To calculate the rate of evaporation caused by the medicine, we need to determine the amount of heat energy that was removed from the child's body and then divided by the time it took for the temperature to drop.
We know that the specific heat of the human body is 4.2 J/g/°C, which means that it takes 4.2 joules of energy to raise the temperature of 1 gram of body mass by 1 degree Celsius.
First, we need to calculate the amount of heat energy that was removed from the child's body:
Q = mcΔT
Where:
Q = amount of heat energy (in joules)
m = mass of the child's body (in grams)
c = specific heat of the human body (in J/g/°C)
ΔT = change in temperature (in °C)
Converting the units and plugging in the values:
Q = (20 kg * 1000 g/kg) * (4.2 J/g/°C) * (-4 °C)
Q ≈ -336,000 J
The negative sign indicates that heat energy was removed from the body.
Next, we need to calculate the amount of heat energy that was converted into the evaporation process, which is given by the latent heat of vaporization:
Q = mlv
Where:
lv = latent heat of vaporization (in J/g)
Plugging in the value:
-336,000 J = m * 2436 J/g
m ≈ -138 g
Again, the negative sign indicates that mass was lost due to evaporation.
Finally, we can calculate the rate of evaporation by dividing the mass lost by the time it took to lose that mass:
Rate of evaporation = (mass lost) / (time taken)
Rate of evaporation ≈ (-138 g) / (25 min)
Rate of evaporation ≈ -5.52 g/min
Therefore, the rate of evaporation caused by the medicine is approximately 5.52 grams per minute.