THC_Conservation of Energy Lesson

Conservation of Energy

You just learned that energy can be transferred from system to its surroundings (or vice versa) through heat transfer or by work. Always remember that heat and work are processes. So, it is not correct to ask how much heat or work a system has. Instead, you can ask questions like, "How much work was done?" or "How much heat is required?" If you go ahead and get in the habit of speaking about these terms correctly, you are less likely to make a mistake about these concepts.

Now that you know the meaning of heat and work, let's talk about how they are related to each other.  

You already know that the total energy of a system is a combination of all the kinetic and potential energies of that system. We call this the law of conservation of energy. We cannot actually measure all of these values on an atomic level, but we can measure changes in the total energy. This is where heat and work come in. Since they are the processes by which energy changes, the change in internal energy of a system is equal to the combination of the heat exchanged and the work done. The total internal energy cannot be created or destroyed, only transformed. This is known as the 1st Law of Thermodynamics.

1st LAW of THERMODYNAMICS ΔU = q + w U is the symbol for internal energy

Now let's look at the positive and negative signs that we must associate with heat, work, and energy and what they mean.

So, if heat is positive, it means that energy is added to the system (from the surroundings).

+q = heat added to the system 

If heat is negative, it means that energy is leaving the system (flowing to the surroundings).

-q = heat removed from the system

If work is positive, it means that energy is put into the system. In science we often refer to this as work being done on the system. Compression of a gas is an example of work being done on the system.

+w = work done on the system

If work is negative, it means that energy is removed from the system.   In science we often refer to this as work being done by the system. Expansion of a gas is an example of work being done on the system.

-w = work done by the system

The following visual summarizes the meaning of the signs for heat and work.

A positive value indicates that energy has been added. A negative value means that energy has been removed or lost. But, we need to specify our perspective. We will always evaluate energy from the perspective of the system, not the surroundings. Sometimes, you will read problems that speak from the perspective of the surroundings. You must flip these around when assigning + and - signs in order to use them properly in the equations.

heat, q +q means heat is absorbed by the system -q means heat is released by the system work, w +w means work is done on the system -w means work is done by the system

Since in an isolated system, the internal energy won't change, we can use this concept and the equation for internal energy to solve some simple problems.   However, don't be fooled by the simplicity of the math here.   These type questions are very commonly confused because students don't pay attention to the language of the problem and don't apply the appropriate signs to work and heat.

Example #1 If an isolated system does 10 J of work (by expanding the volume of a piston), how much heat was added? AU = q + w Since work was done by the system, w is negative. Since the system is isolated, ΔU = 0. 0 = q + -10 q = 10 J +q indicates that heat was added. This agrees with the language in the problem.

Example #2 If 5 J of heat is removed and 1 J of work is done on the system (compression), what is the change in the internal energy? Since heat is removed, q is -. Since work is done on the system, w is +. ΔU = q + w ΔU = -5 ++1 ΔU = -4 J

Note: You will sometimes see the equation for the 1st Law of Thermodynamics written as ∆U = q - w. In this case, the equation is only written for work done by the system. Since we use a negative sign to indicate work done on a system, we don't need to write the equation this way! But, pay attention to this possibility as you practice problems from different sources. 

Let's take a moment and look back at the equation we derived for pressure-volume work. We did not take into consideration positive or negative signs and left the equation with an absolute value sign. W = PΔV w What sign will we get for work for the compression of a gas? We always calculate AV as Vfinal - Vinitial. In a compression Vfinal will be smaller than Vinitial, resulting in a negative AV. If we plug this into the equation above, what sign do we get for work? ?= PΔV Pressure values are always positive. In compression, AV is negative. PΔV = (+)(-) This gives us a negative value for work. But, in a compression, the volume of the gas decreases because work is done on the gas. We just learned that when work is done on the system, w is positive. So, our equation for pressure-volume work must be corrected. The adjusted equation is: W = - PΔV This negative sign in this equation simply makes it so that the values calculated for work match the convention.

Example Find the amount of work done by the system when 1 liter of an ideal gas, initially at a pressure of 10 atm, is allowed to expand at constant temperature to 10 liters by reducing the external pressure to 1 atm. Before you even start the problem, think about what expansion means. Expansion means that work is being done expect work to be calculated as a So, we value. To calculate work, use the equation w=-PΔV We do not need to know the original pressure to solve for the work done. So, P = 1 1 atm. ΔV = Vfinal - Vinitial = 10 L-1 L w = - (1 atm)(9 L) w=-9 atmL The unit (atm)(L) is an acceptable unit for work, but it is not equivalent to a Joule. If you are asked to present your answer in J, the standard unit for work, use the conversion 1 Latm = 101 J. Note that the question could have been written as: Find the amount of work done on the surroundings... The answer would not change however! Work done on the surroundings is the same as work done by the system. The equations that we use are written from the perspective of the system!

Remember to work on the module practice problems as you complete each section of content.

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