A physicist converted 2kg of water at 37 degrees Celsius to steam at 100 degrees Celsius.
Assuming no heat is lost, calculate the amount of energy needed
(i) to heat the water at 100 degrees
(ii) to heat the water from 100 degrees Celsius to steam at 100 degrees Celsius
(iii) to completely convert the water from 37 degrees Celsius to steam at 100 degrees Celsius
Well, I have to admit, that's a lot of heat you're talking about! But fear not, for I, Clown Bot, am here to calculate the amount of energy needed for each step:
(i) To heat the water from 37 degrees Celsius to 100 degrees Celsius, we need to calculate the heat energy using the formula Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. So, m = 2 kg, c = 4.18 kJ/kg°C (specific heat capacity of water), and ΔT = 100 - 37 = 63°C.
Plugging in the values, we have Q = (2 kg)(4.18 kJ/kg°C)(63°C) = 526.68 kJ.
(ii) To heat the water at 100 degrees Celsius to steam at 100 degrees Celsius, we need to calculate the heat energy using the formula Q = mL, where Q is the heat energy, m is the mass, and L is the latent heat of vaporization. The latent heat of vaporization for water is 2260 kJ/kg.
Plugging in the values, we have Q = (2 kg)(2260 kJ/kg) = 4520 kJ.
(iii) To completely convert the water from 37 degrees Celsius to steam at 100 degrees Celsius, we simply add up the energies calculated in steps (i) and (ii): 526.68 kJ + 4520 kJ = 5046.68 kJ.
So, the total amount of energy needed to convert the water from 37 degrees Celsius to steam at 100 degrees Celsius is 5046.68 kJ. Phew! That's a lot of energy! Better keep the kettle handy!
To calculate the amount of energy needed for each step, you can use the specific heat formula and the heat of vaporization formula.
(i) To heat the water at 37 degrees Celsius to 100 degrees Celsius, you need to calculate the energy required using the specific heat formula:
Q = mcΔT
where:
Q = energy in joules
m = mass of water (2 kg)
c = specific heat capacity of water (4.18 J/g°C)
ΔT = change in temperature (100°C - 37°C)
First, convert the mass of water from kg to grams:
m = 2 kg * 1000 g/kg = 2000 g
Now, substitute these values into the formula:
Q = 2000 g * 4.18 J/g°C * (100°C - 37°C)
= 2000 g * 4.18 J/g°C * 63°C
= 527,760 J
Therefore, the amount of energy needed to heat the water from 37 degrees Celsius to 100 degrees Celsius is 527,760 joules.
(ii) To heat the water from 100 degrees Celsius to steam at 100 degrees Celsius, the temperature remains constant, so the energy required is zero.
(iii) To completely convert the water from 37 degrees Celsius to steam at 100 degrees Celsius, you need to calculate the energy required using the heat of vaporization formula:
Q = mL
where:
Q = energy in joules
m = mass of water (2 kg)
L = heat of vaporization of water (2,260,000 J/kg)
Substitute the values into the formula:
Q = 2 kg * 2,260,000 J/kg
= 4,520,000 J
Therefore, the amount of energy needed to completely convert the water from 37 degrees Celsius to steam at 100 degrees Celsius is 4,520,000 joules.
To calculate the amount of energy needed to perform the tasks described, we can use the formula:
Q = m * c * ΔT
where:
Q is the amount of energy needed,
m is the mass of the substance,
c is the specific heat capacity of the substance,
ΔT is the change in temperature.
(i) To heat the water at 100 degrees Celsius, we need to calculate the energy needed to increase the temperature from 37 degrees Celsius to 100 degrees Celsius.
First, let's calculate the energy needed to increase the temperature of 2kg of water from 37 degrees Celsius to 100 degrees Celsius.
ΔT = 100 degrees Celsius - 37 degrees Celsius = 63 degrees Celsius
The specific heat capacity of water is 4.186 J/g°C (or 4186 J/kg°C).
Converting the mass from kg to grams:
m = 2kg * 1000g/kg = 2000g
Using the formula, we can calculate the amount of energy needed:
Q = m * c * ΔT
Q = 2000g * 4.186 J/g°C * 63°C
(ii) To heat the water from 100 degrees Celsius to steam at 100 degrees Celsius, we need to calculate the energy needed to change the state of water without changing its temperature.
The heat of vaporization of water is 2260 J/g.
Using the formula, we can calculate the amount of energy needed:
Q = m * L
Q = 2000g * 2260 J/g
(iii) To completely convert the water from 37 degrees Celsius to steam at 100 degrees Celsius, we need to add the energy calculated in (i) and (ii).
Total energy needed = Energy needed in (i) + Energy needed in (ii)
Please substitute the values into the formulas to calculate the final answers.