 ###### Kendal Orenstein

Rutger's University
M.Ed., Columbia Teachers College

Kendal founded an academic coaching company in Washington D.C. and teaches in local area schools. In her spare time she loves to explore new places.

Problem 1

# Specific Heat - Concept

Kendal Orenstein ###### Kendal Orenstein

Rutger's University
M.Ed., Columbia Teachers College

Kendal founded an academic coaching company in Washington D.C. and teaches in local area schools. In her spare time she loves to explore new places.

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Specific heat is the amount of heat required to raise one gram of any substance one degree Celsius or Kelvin. The formula for specific heat is the amount of heat absorbed or released = mass x specific heat x change in temperature.

Alright so let's talk about specific heat, specific heat we're going to denote with a letter c. It's the amount of heat required to raise the temperature of 1 gram of a substance 1 degrees Celsius or 1 Kelvin. The reason these can be interchanged is because they have the same incremental values they can be switched around. Alright so when we're talking abut heat we're actually measuring heat and energy and let's talk about the numbers that you're actually going to be seeing in the units so we measure energy in Calories or joules. So 1 Calorie equals 4.184 joules but this is not the Calorie that you see in the back of a food label that's actually Calorie with a capital C that's actually 1 kilo Calorie and those equal a thousand Calories or 4,184 joules. So understanding what these numbers mean when talking about heat, let's go back to talking about specific heat and that is measured in joules per gram degrees Celsius.

Let's talk about the specific heat of water, water has a specific heat of 4.184 joules per gram degrees Celsius and what does that mean? That means for every gram of water you have that you want raise 1 degrees Celsius it require 4.184 joules of energy. That's actually relatively high compared to the rest of the things in this table and most substances actually. That's because it takes a lot of energy to heat up water, if you think about when you're boiling water on the stove or something it actually takes a long time and a lot heat for it to actually raise from, go from liquid state up to when it reaches the gaseous state. Ice in specific heat is actually different for each state of matter so ice to actually raise the temperature of ice it'll only take 2.03 joules of heat to raise 1 gram of substance 1 degree Celsius.

And steam is the same way, it only takes 2.01 so it's half as much energy to raise the temperature of ice or steam versus water. Aluminum is also actually relatively high compared to other metals. Metals have usually, typically very low specific heat value. But aluminum is actually pretty high at 0.897 joules per gram degree Celsius so the lower the number the easier it is for it to heat up. Okay so when we use this in actual formulas and to actually talk about the amount of heat needed or how much temperature shifted or how much mass we needed for certain substances. So we're going to use this formula q equals mc delta t or q equals m cad. q is, when we're talking about heat is a symbol for heat and are usually measured in joules could be measured in kilo joules or calories that doesn't make a difference, but this is q represents the amount of heat needed or heat required or energy.

m is our symbol for mass is usually measured in grams, c is our specific heat of that particular substance and delta t is the change it can be again, it can be in either Kelvin or degrees Celsius it doesn't make a difference because it's the change in heat. Now let's talk about how this affects the phase change diagram. Okay this is a phase change diagram for water, let me write that down. Okay so notice if you look at the slopes for the change in energy as the increased temperature of a solid versus liquid. Notice solid has a steeper slope than liquid, that's because liquid requires more energy to increase the temperature for gram than it does with solid or gas. These are actually steeper in slopes than it is for a liquid, so this actually affects the phase change diagram as well and that's because of the specific heat.

Let's go over and solve a problem together and figure out how this actually affects other things. So we have an architect and he is actually really interested in sustainable energy. So an architect designs a house that is partially heated by solar energy, heat from the sun will be stored in a solar pond similar to that other swimming pool. So we have this pond that we're dealing with. It's made up of 14,500 kilograms of granite rock and then inside that it contains 22,500 kilograms of water. Alright together the granite and the water absorb heat during the day and release it at night, which then they release at night into the house, heating the house at night. The architect found that the solar pond increases 22 degrees Celsius during the day and lowers at 22 degrees Celsius at night. So how much energy does it release and absorb during the day? So let's underline what we, the information that we have.

Let's start with water, since we have 2 substances granite and water, the amount of energy it actually requires, the total amount of energy is going to be the q of granite plus the q of H2O plus, with the q we know equals mc delta t. Okay so let's first deal with water, okay well water well water we have the mass is 22,500 kilograms and we want it in grams. So we're going to make it 2.25 times 10 to the seventh grams okay. The c of water or the specific heat of water is 4.184 joules per gram degrees Celsius. Now the reason I wanted this even in grams and I couldn't use kilograms is because my unit for specific heat had grams in it. So I want to make sure these units are the same, okay. So then we're going to, we know that it changes the temperature it increases and decrease in temperature 22 degrees Celsius. So our change in temperature is 22 degrees Celsius.

Okay so when I multiply these all together I get the amount of energy that's required or that is absorbed by solar pond [IB] water that's in the solar pond. And so we multiply these together and we get 2.1 times 10 to the ninth joules and the reason is because again specific heat is measured in joules or this q is measured in joules. Okay let's talk about the q for granite because the pool is made up of water and granite. The mass of the water is 14 I'm sorry the mass of the granite is 14,500 kilograms which is 1.45 times 10 to the seventh grams. The q for granite if you look at our table is 0.803 and again that's changing 22 degrees Celsius. And I'm just not putting the units because I want to save some space. Alright when I multiply these all together I get 2.4 sorry that's not true I'm sorry about that I get 2.6 times 10 to the eighth joules. Okay so the total amount of energy that this actual solar pool gains and this is in a day is 2. We're going to add this up 2.4 times 10 to the ninth joules of energy. So this actually saves us a lot of energy when we're dealing with, when we're actually going to heat up or cool down our house. So we're saving a lot of money in sustainable energy by using the solar pool. So specific heat actually tells us a lot of different things and it's unique for each specific substance and it's the amount of energy required to raise 1 gram of a substance, 1 degree Celsius.