Because of the pressure inside a popcorn kernel, water does not vaporize at 100°C. Instead, it stays liquid until its temperature is about 175°C, at which point the kernel ruptures and the superheated water turns into steam. How much energy is needed to pop 95.0 g of corn if 12 percent of a kernel's mass consists of water: Assume that the latent heat of vaporization of water at 175°C is 0.90 times its value at 100°C and that the kernels have an initial temperature of 175°C.
The energy needed to pop 95.0 g of corn is approximately 5.2 kJ.
First, calculate the mass of water in the kernels:
Mass of water = 95.0 g x 0.12 = 11.4 g
Next, calculate the latent heat of vaporization of water at 175°C:
Latent heat of vaporization = 0.90 x 2256 kJ/kg = 2030 kJ/kg
Finally, calculate the energy needed to pop the kernels:
Energy needed = (11.4 g x 2030 kJ/kg) / 1000 = 5.2 kJ
To find the amount of energy needed to pop 95.0 g of corn, we need to consider several factors: the mass of water in the corn kernels, the latent heat of vaporization of water, and the change in temperature required to pop the kernels.
Let's break down the steps:
Step 1: Find the mass of water in the corn kernels.
Since 12 percent of a kernel's mass consists of water, we can calculate the mass of water in 95.0 g of corn by multiplying the total mass by the percentage of water:
Mass of water = 0.12 * 95.0 g
Step 2: Calculate the latent heat of vaporization of water at 175°C.
Given that the latent heat of vaporization of water at 100°C is the reference, we can use the given information that it is 0.90 times its value at 100°C. Therefore, the latent heat of vaporization at 175°C is 0.90 times the reference value.
Step 3: Determine the change in temperature required to pop the kernels.
The initial temperature of the kernels is already given as 175°C. This means we don't need to calculate any temperature change.
Step 4: Calculate the energy required to pop the corn.
The energy required can be found using the formula:
Energy = mass of water * latent heat of vaporization
Plug in the values we've determined so far:
Energy = (0.12 * 95.0 g) * (0.90 * latent heat of vaporization)
To calculate the exact value, we need to know the reference value for the latent heat of vaporization at 100°C. Once we have that, we can substitute it into the equation and calculate the energy needed to pop 95.0 g of corn.
To calculate the energy needed to pop 95.0 g of corn, we need to consider the energy required to heat up the corn kernels and the energy required to vaporize the water inside the kernels.
Step 1: Calculate the mass of water in the 95.0 g of corn.
Given that 12 percent of a kernel's mass consists of water, we can calculate the mass of water as follows:
Mass of water = (12/100) * 95.0 g
Step 2: Calculate the energy required to heat up the corn kernels.
The specific heat capacity of corn is approximately 0.35 J/g°C.
Assuming an initial temperature of 175°C and a final temperature of 175°C (since we are assuming the kernels have an initial temperature of 175°C), there is no change in temperature. Therefore, no energy is needed to heat up the corn kernels.
Step 3: Calculate the energy required to vaporize the water.
The latent heat of vaporization of water is the amount of energy required to transform water from a liquid to a gas at constant temperature. Given that the latent heat of vaporization of water at 100°C is reduced to 0.90 times its value at 175°C, we need to consider this value.
Let's assume the latent heat of vaporization of water at 100°C is L. Then, the latent heat of vaporization of water at 175°C is 0.90L.
The energy required to vaporize the water can be calculated as follows:
Energy = (mass of water) * (latent heat of vaporization of water at 175°C)
Substituting the values, we have:
Energy = (mass of water) * (0.90L)
Step 4: Substitute the values and calculate the energy required.
Substituting the values from Step 1 and Step 3, we can calculate the energy required as follows:
Energy = [(12/100) * 95.0 g] * (0.90L)
Note: We do not have the exact value for L. You will need to find the latent heat of vaporization of water at 100°C and then calculate 0.90 times that value to determine the latent heat of vaporization at 175°C. Once you have that value, you can substitute it into the equation above to calculate the final energy required to pop the 95.0 g of corn.