Optics: How much light required to heat water?

That is why scientific notation is used. The only exception would be if there was a notation after the number, like '234,719 grams, significant to the nearest gram'.
  • #1
Feodalherren
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Homework Statement


How many grams of water could have its temperature raised by 1.13 °C by a mole of photons that have a wavelength of 510 nm?


Homework Equations



E=hf

λf=c

The Attempt at a Solution



(3x10^8) / (510 x 10^-9) = 5.88 x 10^14 Hz

multiply by Planck's constant to get E= 3.8977x10^-19 J/photon.

Now multiply by avogadro's number to get 234719J

234,719J = m (4.18J/g C)(1.13 C)

m = 49693g

supposedly not the correct answer. I don't know the correct answer but the input thing for online homework tells me it wants 3 significant figures in grams and since you can't enter any powers of ten the answer must be less than a kg.
Any ideas?
 
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  • #2
Your work looks correct to me.

It could be that they want you to round to three significant figures without using scientific notation (powers of 10). Zeros on the right end of the number would be assumed non-significant.
 
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  • #3
Hah! You were right. That just doesn't seem like the correct way to do it to me though.

Thank you.
 
  • #4
Good. I agree with you. Zeros on the right of an integer are generally ambiguous in regard to being significant figures.
 
  • #5


This is a complex question that requires a thorough understanding of optics and thermodynamics. The amount of light required to heat water depends on various factors such as the intensity of the light, the efficiency of the heating process, and the specific heat capacity of water. Additionally, the wavelength of the light also plays a role in determining the amount of energy absorbed by water.

In this case, the given information about the wavelength of the photons and their energy is correct. However, the calculation of the mass of water that can be heated by a mole of photons is incorrect. It is important to note that the energy of a mole of photons is actually 3.8977x10^5 J, not 3.8977x10^-19 J as calculated. This is because one mole of photons contains Avogadro's number (6.022x10^23) of photons.

Using the correct value for the energy of a mole of photons, we can calculate the mass of water that can be heated by this amount of energy. Using the equation Q = mcΔT, where Q is the heat energy, m is the mass of water, c is the specific heat capacity of water (4.18 J/g°C), and ΔT is the change in temperature, we can rearrange the equation to solve for the mass of water.

m = Q / (cΔT) = (3.8977x10^5 J) / (4.18 J/g°C x 1.13°C) = 87021g = 87.02kg

Therefore, a mole of photons with a wavelength of 510nm can heat approximately 87.02kg of water by 1.13°C. It is important to note that this calculation is based on ideal conditions and does not take into account any losses in energy during the heating process. The actual amount of water that can be heated may be slightly lower than this value.

In conclusion, the amount of light required to heat water depends on various factors and cannot be determined solely based on the wavelength of the photons. A more accurate calculation would require additional information such as the intensity of the light and the efficiency of the heating process.
 

1. How does light affect the temperature of water?

Light can increase the temperature of water through the process of absorption. When light is absorbed by water molecules, it causes the molecules to vibrate, which produces heat and increases the overall temperature of the water.

2. What type of light is most effective in heating water?

The type of light that is most effective in heating water is infrared light. This type of light has longer wavelengths and is able to penetrate deeper into the water, causing more water molecules to vibrate and produce heat.

3. How much light is needed to heat a specific amount of water?

The amount of light needed to heat water depends on several factors such as the intensity of the light, the type of light, and the starting temperature of the water. In general, it takes about 4 joules of energy to raise the temperature of 1 gram of water by 1 degree Celsius.

4. Can different colors of light affect the temperature of water differently?

Yes, different colors of light can affect the temperature of water differently. This is because different colors have different wavelengths and energy levels. For example, red light has longer wavelengths and lower energy levels, making it less effective in heating water compared to blue light which has shorter wavelengths and higher energy levels.

5. Is it possible to heat water solely using light?

Yes, it is possible to heat water solely using light. This process is known as photothermal heating and is commonly used in solar water heaters. However, it requires a significant amount of light and may not be as efficient as traditional methods of heating water, such as using electricity or gas.

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