You are helping a friend who is a veterinarian to do some minor surgery on a cow

Question

You are helping a friend who is a veterinarian to do some minor surgery on a cow. She has asked you to sterilize a scalpel and a hemostat by boiling them for 30 minutes. You boil them as ordered and then quickly transfer the instruments to a well insulated tray containing 200 grams of sterilized water at room temperature (23 °C) which is just enough to cover the instruments. After a few minutes the instruments and water will come to the same temperature, but will they be safe to hand to your friend without being burned? You are both wearing surgical rubber gloves, but they are very thin. You know that both the 50 gram scalpel and the 70 gram hemostat are made from steel which has a specific heat of 450 J / (kg °C). They were boiled in 2.0 kg of water with a specific heat of 4200 J / (kg °C).

Explanation / Answer

We need conservation of energy. The heat lost by the scalpel and hemostat will be gained by the room temp water

The scalpel and hemostat are going to be at 100 C initially from the boiling water

The formula that applies is Q = mc(delta T)

mc(delta T)hemostat + mc(delta T)scalpel = mc(delta T)water

(.07)(450)(100 - Tf) + (.05)(450)(100 - Tf) = (.2)(4200)(Tf - 23)

3150 - 31.5Tf + 2250 - 22.5 Tf = 840Tf - 19320

5400 - 54Tf = 840Tf - 19320

24720 = 894Tf

Tf = 27.6o C (Which is 81.9o F)

That is definitely safe to handle.

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