You want to heat 200 g of water in your microwave oven. The water is initially at 15°C, and you would like to heat it to 90°C. The microwave oven emits microwave radiation at a frequency of 2560 MHz. Water has a specific heat of 4186 J/kg°C.

How many photons must the water absorb?

Question

02-01-2024
Physics

College

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You want to heat 200 g of water in your microwave oven. The water is initially at 15°C, and you would like to heat it to 90°C. The microwave oven emits microwave radiation at a frequency of 2560 MHz. Water has a specific heat of 4186 J/kg°C.

How many photons must the water absorb?

Answer :

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pankajprajapati1470 pankajprajapati1470 · Answer 1 · 2024-09-25T23:05:48-04:00

Final answer:

To heat 200 g of water from 15°C to 90°C, approximately 3.91 x 10²⁹ photons must be absorbed by the water, considering the energy of each photon as 1.0 x 10⁻⁵ eV and the specific heat of water as 4.186 J/g°C.

Explanation:

The first step is to calculate the energy required to heat the water. This can be done using the equation Q = mcΔT, where m is the mass of the water, c is the specific heat of water and ΔT is the change in temperature. So, Q = 200 g * 4.186 J/g°C * (90°C - 15°C) = 627000 J.

Next, we need to convert this energy to electron volts (eV), as the energy of the photons will be given in eV. Since 1 J = 6.242 x 10¹⁸ eV, the energy required is 627000 J * 6.242 x 10¹⁸ eV/J = 3.91 x 10²⁴ eV.

Lastly, as each photon absorbed by a water molecule has an energy of 1.0 x 10⁻⁵ eV, the number of photons required is 3.91 x 10²⁴ eV / 1.0 x 10⁻⁵ eV/photon = 3.91 x 10²⁹ photons.

Learn more about Calculation of Absorbed Photons here:

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You want to heat 200 g of water in your microwave oven. The water is initially at 15°C, and you would like to heat it to 90°C. The microwave oven emits microwave radiation at a frequency of 2560 MHz. Water has a specific heat of 4186 J/kg°C.How many photons must the water absorb?

Answer :

Final answer:

Explanation:

Other Questions

You want to heat 200 g of water in your microwave oven. The water is initially at 15°C, and you would like to heat it to 90°C. The microwave oven emits microwave radiation at a frequency of 2560 MHz. Water has a specific heat of 4186 J/kg°C.

How many photons must the water absorb?