Question

Свет с длинной волны 0,3 мкм падает на прозрачную кювету с водой. В результате вода в кювете нагрелась на 15 градусов за 15 минут. Известно что источник света излучает 2* степени фотонов в секунду. Найти массу воды в кювете. Считать, что все падающее световое излучение идет на нагрев воды.

Answer 1

Ответ:

Объяснение:

Энергия одного падающего фотона:

ε = h·c / λ = 6,63·10⁻³⁴·3·10⁸ / (0,3·10⁻⁶) ≈ 6,63·10⁻¹⁹ Дж

За 15 минут поглощается энергия:

Q = 6,63·10⁻¹⁹·2·10²⁰·15·60 ≈ 120 000 Дж

Масса воды:

m = Q / (c·Δt) = 120 000 / (4200·15) ≈ 1,9 кг

Answer 2

Calculation of the Mass of Water in the Cuvette

To calculate the mass of water in the cuvette, we need to consider the energy absorbed by the water from the incident light and the specific heat capacity of water.

The energy absorbed by the water can be calculated using the formula:

Energy absorbed = Power of the light source * Time

Given that the light source emits 2*10^2 photons per second, we can calculate the power of the light source as follows:

Power of the light source = Number of photons emitted per second * Energy per photon

To find the energy per photon, we can use the equation:

Energy per photon = Planck's constant * Speed of light / Wavelength

Given that the wavelength of the light is 0.3 μm (micrometers), we can substitute the values into the equation to find the energy per photon.

Once we have the power of the light source, we can calculate the energy absorbed by the water using the formula mentioned earlier.

To find the mass of water, we can use the equation:

Energy absorbed = Mass of water * Specific heat capacity of water * Temperature change

Given that the temperature change is 15 degrees Celsius and the time is 15 minutes, we need to convert the time to seconds before using it in the equation.

Let's calculate the mass of water in the cuvette using the above information.

Calculation Steps:

1. Calculate the energy per photon: - Wavelength = 0.3 μm - Planck's constant = 6.626 x 10^-34 J·s - Speed of light = 3 x 10^8 m/s

Energy per photon = (Planck's constant * Speed of light) / Wavelength

2. Calculate the power of the light source: - Number of photons emitted per second = 2 * 10^2 photons/s

Power of the light source = Number of photons emitted per second * Energy per photon

3. Calculate the energy absorbed by the water: - Time = 15 minutes = 15 * 60 seconds

Energy absorbed = Power of the light source * Time

4. Calculate the mass of water: - Specific heat capacity of water = 4.18 J/g·°C - Temperature change = 15 degrees Celsius

Energy absorbed = Mass of water * Specific heat capacity of water * Temperature change

Let's perform the calculations step by step.

Calculation:

1. Calculate the energy per photon: - Wavelength = 0.3 μm - Planck's constant = 6.626 x 10^-34 J·s - Speed of light = 3 x 10^8 m/s

Energy per photon = (6.626 x 10^-34 J·s * 3 x 10^8 m/s) / (0.3 x 10^-6 m)

Energy per photon = 6.626 x 10^-19 J

2. Calculate the power of the light source: - Number of photons emitted per second = 2 * 10^2 photons/s

Power of the light source = (2 * 10^2 photons/s) * (6.626 x 10^-19 J/photon)

Power of the light source = 1.3252 x 10^-16 J/s

3. Calculate the energy absorbed by the water: - Time = 15 minutes = 15 * 60 seconds

Energy absorbed = (1.3252 x 10^-16 J/s) * (15 * 60 s)

Energy absorbed = 1.19368 x 10^-13 J

4. Calculate the mass of water: - Specific heat capacity of water = 4.18 J/g·°C - Temperature change = 15 degrees Celsius

Energy absorbed = Mass of water * Specific heat capacity of water * Temperature change

1.19368 x 10^-13 J = Mass of water * 4.18 J/g·°C * 15°C

Mass of water = (1.19368 x 10^-13 J) / (4.18 J/g·°C * 15°C)

Mass of water ≈ 5.68 x 10^-13 g

Therefore, the mass of water in the cuvette is approximately 5.68 x 10^-13 grams.

Please note that the above calculation assumes that all the incident light is absorbed by the water and that there are no other factors affecting the heating of the water.