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I was thinking about this problem when I searched up how warm it takes to kill the new coronavirus. A source said 132 fahrenheit for 30 minutes. I wanted to calculate how much energy that would take so then I could easily find out how long I would have to microwave an object to get the same results.

All I want is just how much energy is put into maintaining this 132 fahrenheit for half an hour at a room temperature. A formula would be fine because I want to be able to apply this to other problems that might come up.

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Your question cannot be answered without more details - as posted, the answer is 0, infinite, or anything in between.

  • If the water is perfectly insulated, it will forever stay at its current temperature, so you need zero energy.
  • If the water is connected with a perfect conductor (which is connected to the outside, which has a lower temperature), you need to provide an infinite amount of energy - basically, you will not be able to heat it fast enough.
  • for various real-world materials, the result can be calculated using their conductivity K, the temperature difference ΔT to the outside , and their surface area. You would need to define for example ‘the water is in a ceramic bowl of 2 sq ft area, 1/4 in thick, and on top is 1 sq ft air at 72 F’, etc.
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The amount of energy required to maintain water at some temperature over some time is simply equal to the amount of energy that the water loses to the environment over that time.

It depends on the conditions that the water is in, specifically how much heat the water is losing the environment. For example, it will take more energy to maintain water at 132 F when you place it in a cold windy environment because it's losing lots of heat in that environment.

So let's say you have a simple scenario of a pot of water sitting in room temperature. A simple energy balance on your water gives:

$$ q_{in} = hA_s(T-T_0) $$

Where $q_{in}$ is the input power, $h$ is an effective heat transfer coefficient telling how much heat the water loses to the ambient (typical value of 5-10 $W/m^2K$ for a 56 C object sitting in a room with no wind), $A_s$ is the surface area of your water container, $T$ is the temperature of the water (56 C), and $T_0$ is room temperature (25 C).

So, all you need is the surface area of your water container. Then solve for the required power $q_in$, and multiply by time (30 min) to get the required energy.

$$ Q_{in} = tq_{in} $$

Where $t$ is the time you desire (30 min). That's how you do it.

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