# How much boiling water would you need to raise the bath to body temperature (about 37 ∘C)? Assume that no heat is transferred to the surrounding environment. Express your answer to two significant figures and include the appropriate units.

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You fill your bathtub with 25 kg of room-temperature water (about 25 ∘C). You figure that you can boil water on the stove and pour it into the bath to raise the temperature.

You fill your bathtub with 25 kg of room-temperature water (about 25 ∘C). You figure that you can boil water on the stove and pour it into the bath to raise the temperature.

The idea here is that the heat given off by the boiling water will be equal to the heat absorbed by the room-temperature sample.

The minus sign is used here because, by convention, heat given off carries a minus sign.

Another assumption that you have to make is that the specific heat of liquid water is constant regardless of the temperature of the liquid water.

In other words, you need to have

Now, your tool of choice here will be the equation

Here

So, you know that you have

for the room-temperature water, which has

Similarly, you have

for the boiling water, which has

This is equivalent to

Plug in your values to find

Notice that you need the minus sign to cancel out the minus sign coming from the change in temperature.

The answer is rounded to two sig figs.

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You would need approximately twice the volume of water as the volume of the bath.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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