Question

Электромагнитное излучение с длиной волны 3,3×10^–7 м используется для нагревания воды. Какую массу воды можно нагреть за 700 с на 10оС, если источник излучает 10^20 фотонов за 1 с? Считать, что излучение полностью поглощается водой.

Answer 1

Q=N*h*c*t/L=10^20*6,6*106-34*3*10^8*700/3,3*10^-7=42*10^3 Дж
m=Q/C*dt=42*10^3/4200*10=1 кг

Answer 2

Calculation of the Mass of Water Heated by Electromagnetic Radiation

To calculate the mass of water that can be heated by electromagnetic radiation with a wavelength of 3.3×10^–7 m for a duration of 700 s and a temperature increase of 10°C, we need to consider the energy absorbed by the water.

The energy of a photon can be calculated using the equation:

E = hf

Where: - E is the energy of the photon - h is Planck's constant (6.62607015 × 10^-34 J·s) - f is the frequency of the radiation

Since we are given the wavelength (λ) of the radiation, we can calculate the frequency (f) using the equation:

c = λf

Where: - c is the speed of light (3 × 10^8 m/s)

By rearranging the equation, we can solve for f:

f = c / λ

Now, we can calculate the energy of one photon using the equation:

E = hf = hc / λ

Where: - h is Planck's constant (6.62607015 × 10^-34 J·s) - c is the speed of light (3 × 10^8 m/s) - λ is the wavelength of the radiation (3.3×10^–7 m)

To find the total energy absorbed by the water, we need to multiply the energy of one photon by the number of photons emitted by the source in 1 second:

Total energy absorbed = (Energy of one photon) × (Number of photons emitted per second)

Given that the source emits 10^20 photons per second, we can calculate the total energy absorbed.

Finally, we can use the specific heat capacity of water to calculate the mass of water heated by the absorbed energy.

Calculation Steps:

1. Calculate the frequency of the radiation: - Using the equation: f = c / λ - Substitute the values: c = 3 × 10^8 m/s and λ = 3.3×10^–7 m - Calculate: f = (3 × 10^8 m/s) / (3.3×10^–7 m)

2. Calculate the energy of one photon: - Using the equation: E = hf = hc / λ - Substitute the values: h = 6.62607015 × 10^-34 J·s, c = 3 × 10^8 m/s, and λ = 3.3×10^–7 m - Calculate: E = (6.62607015 × 10^-34 J·s) × (3 × 10^8 m/s) / (3.3×10^–7 m)

3. Calculate the total energy absorbed by the water: - Using the equation: Total energy absorbed = (Energy of one photon) × (Number of photons emitted per second) - Substitute the values: Energy of one photon (calculated in step 2) and Number of photons emitted per second = 10^20 - Calculate: Total energy absorbed = (Energy of one photon) × (10^20)

4. Calculate the mass of water heated by the absorbed energy: - Use the specific heat capacity of water, which is approximately 4.18 J/g°C - The formula for calculating the energy absorbed by water is: Energy = mass × specific heat capacity × temperature change - Rearrange the formula to solve for mass: mass = Energy / (specific heat capacity × temperature change) - Substitute the values: Energy (calculated in step 3), specific heat capacity = 4.18 J/g°C, and temperature change = 10°C - Calculate: mass = Energy / (4.18 J/g°C × 10°C)

Now, let's perform the calculations.