A cook placed five eggs£¬each having a heat capacity of 114J/celcius£¬in a 250g aluminum pot containing 0.5L of water at a temperature of 20celcius. If the heating element is raised at 750W£¬and one fifth of the heat escapes to the surroundings£¬how long will it take the water to boil£¿
To calculate the time it takes for the water to boil, we need to use the formula:
Q = mcΔT
where:
Q is the heat energy required to raise the temperature of the water to its boiling point,
m is the mass of the water,
c is the specific heat capacity of water, and
ΔT is the change in temperature.
Let's calculate the values we need:
Mass of water (m): 0.5L = 500g
Specific heat capacity of water (c): 4.18J/g°C (approximately)
Change in temperature (ΔT): boiling point of water (100°C) - initial temperature (20°C) = 80°C
Now, let's calculate the heat energy required to raise the temperature of the water:
Q = mcΔT
= 500g * 4.18J/g°C * 80°C
= 167,200J
Since one-fifth of the heat escapes to the surroundings, we need to calculate the total heat energy required:
Total heat energy = Q / (4/5)
= 167,200J / (4/5)
= 209,000J
Now let's calculate the time using the power formula:
Power (P) = Energy (E) / time (t)
Rearranging the formula:
Time (t) = Energy (E) / Power (P)
The power (P) is given as 750W, but we need to convert it to Joules per second (W→J/s).
Power (P) = 750W = 750J/s
Now let's calculate the time:
Time (t) = 209,000J / 750J/s
= 278.67 seconds
Therefore, it will take approximately 279 seconds for the water to boil.
To calculate the time it will take for the water to boil, we need to consider the energy required to heat both the water and the eggs, as well as the heat loss to the surroundings.
First, let's calculate the energy required to raise the temperature of the water from 20°C to its boiling point, which is 100°C:
Energy required to heat water = mass of water × specific heat capacity of water × change in temperature
Given:
Mass of water = 0.5 L = 500 g
Specific heat capacity of water = 4.18 J/g°C (approximate value)
Change in temperature = (100°C - 20°C) = 80°C
So, the energy required to heat the water is:
Energy required = 500 g × 4.18 J/g°C × 80°C
Next, let's calculate the energy required to heat the eggs. We know that each egg has a heat capacity of 114 J/°C. Since there are five eggs, the total energy required to heat the eggs is:
Energy required for eggs = 5 eggs × 114 J/°C × 80°C (since both the water and eggs have the same change in temperature)
Now, let's consider the heat loss to the surroundings. We are told that one fifth (1/5) of the heat escapes, so we need to calculate the total energy generated and then reduce it by one-fifth.
Total energy generated by the heating element in 1 second = 750 W × 1 s
Heat loss to surroundings = (1/5) × total energy generated
Now, we need to determine how long it will take to boil the water. We will divide the total energy required for heating both the water and eggs by the net energy generated after accounting for heat loss:
Total energy required = energy required for water + energy required for eggs
Net energy generated = total energy generated - heat loss to surroundings
Finally, we can calculate the time required:
Time required = Total energy required / Net energy generated
Plug in the values into the equations above, and you will get the time required for the water to boil.