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.
To calculate the energy required to pop the corn, we need to consider the energy needed to heat the corn kernels and the energy needed to vaporize the water inside.
Let's break down the problem step by step:
Step 1: Determine 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 = 0.12 × Mass of the corn kernels
= 0.12 × 95.0 g
Step 2: Calculate the heat required to raise the temperature of the corn kernels from 175°C to the boiling point (175°C).
- The specific heat capacity of corn is assumed to be the same as water (4.184 J/g°C). Therefore, the heat required can be calculated as:
Heat for heating the corn kernels = Mass of the corn kernels × Specific heat capacity × Change in temperature
Step 3: Calculate the heat required to vaporize the water inside the corn kernels.
- The latent heat of vaporization at 100°C is not given, but we are told that at 175°C, it is 0.90 times its value at 100°C. Therefore, we can calculate the latent heat of vaporization at 175°C:
Latent heat of vaporization at 175°C = 0.90 × Latent heat of vaporization at 100°C
- Finally, we can calculate the heat required to vaporize the water inside the corn kernels:
Heat for vaporization of water = Mass of water × Latent heat of vaporization at 175°C
Step 4: Calculate the total energy required.
- Add the heat required for heating the corn kernels to the heat required for vaporizing the water to get the total energy:
Total energy = Heat for heating the corn kernels + Heat for vaporization of water
Now, let's plug in the values and calculate the answer:
Step 1: Mass of water
Mass of water = 0.12 × 95.0 g
Step 2: Heat for heating the corn kernels
Heat for heating the corn kernels = Mass of the corn kernels × Specific heat capacity × Change in temperature
Step 3: Heat for vaporization of water
Latent heat of vaporization at 175°C = 0.90 × Latent heat of vaporization at 100°C
Heat for vaporization of water = Mass of water × Latent heat of vaporization at 175°C
Step 4: Total energy
Total energy = Heat for heating the corn kernels + Heat for vaporization of water
By following these steps and plugging in the given values, you can calculate the amount of energy needed to pop 95.0 g of corn.