# Specific heat capacity.The amount of heat lost to the surroundings when 200 g of water freezes at 0 degrees centigrade is utilized to increase the temperature of a liquid by 15 degrees centigrade...

Specific heat capacity.

The amount of heat lost to the surroundings when 200 g of water freezes at 0 degrees centigrade is utilized to increase the temperature of a liquid by 15 degrees centigrade given that the specific heat capacity of the liquid is 2.25 J/(g Kelvin) and latent heat of fusion is (336 J/gm) Find out the mass of the liquid.

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### 1 Answer

This question can be easily answered by splitting the question into two parts:

1) How much heat is released by the freezing of water?

2) Given the increase in temperature, how much mass of mystery liquid do we have?

This is because whenever we have a specific heat in a problem like this, we generally want to calculate the total Joules of heat being transfered between media. This way, we can use the specific heats directly in order to calculate whatever quantity is desired.

**Step 1: Joules of Heat released by Freezing Water**

Thankfully, they give us some easy numbers for this. How are they easy? Well, lots of things in termodynamics are games of cancelling units. We know we have a certain number of grams of water. We also know that latent heat (enthalpy) of fusion is in units of Joules per gram. This tells us (without even needing to look at an equation!) that we just need to multiply the two numbers!

Heat released = 200 g water * 336 Joules / 1 g water

Notice that "grams of water" cancels, giving us 200*336 Joules. So:

Heat released = 200*336 J =** 67.2 kJ released by freezing water**

Now, we can proceed to step 2:

Step 2: Find the mass of mystery fluid

Now, we'll make a significant assumption. We'll say that **ALL **of the heat released by the water is absorbed by the mystery liquid. Now, this never happens in real life...but it's what happens in science problems!

So, if all of the heat absorbed caused an increase in temperature of 15 degrees Kelvin (keep in mind, changes in centigrade/celcius are equivalent to changes in Kelvin), we get the following equation (again by cancelling units to get our answer!):

Mass of liquid = 67.2 kJ absorbed/(2.25 J/(gK)*15 degrees K)

Notice that both the Joules and Kelvin are cancelled out, and by the nature of it's being in the denominator of the denominator, grams is brought to the top to give us a final unit of...Grams!

Mass = 67.2*10^3/(2.25*15) grams = 1991.1 g = **1.99 kg**

And there you have it! Take-away message for thermodynamics, if you don't remember the specific equations, just try to cancel units! Like in this problem, you know you want grams, so you just need to figure out how to cancel out the other units in a way that leaves grams in the numerator.

Hope that helps!

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