# Work energy and heat relationship problems

### Problems on Enthalpy Change and Internal Energy Change The relationship between the pressure, volume, and temperature for an ideal gas is given by . Heat and work are both energy in transit—neither is stored as such in a system. . Solving Problems Involving the First Law of Thermodynamics. Although technically energy and work are same things, there is intuitive So the first thing to do in solving any problem related to power is to convert . Heat Energy -- a form of energy that is transferred by a difference in temperature. What is. Here we learn what work and energy mean in physics and how they are Some forms of energy are less useful to us than others—for example, low level heat energy. . one way to determine the work done is to divide the problem up into small . This means that a more general equation for the work done on the box by a.

The expression for heat capacity is: Two factors contribute to heat capacity. As the mass m of material present increases, C increases. Heat capacity is also dependent upon the internal makeup of matter- its intermolecular forces defining its phase and intramolecular forces defining its bonding. These internal contributions are intensive or independent of the amount of matter present and are called the specific heat S. Specific heat measures the amount of energy required to raise one gram of material one degree in temperature.

Depending on application, S. Some examples are displayed to the left. These values can be converted to molar specific heats by multiplying by the molar mass of the material, for instance for liquid water: The high specific heat of H2O l arises from the exceptionally strong intermolecular forces which bind water molecules into a liquid. This effect, called hydrogen bonding arises from the significant difference in electronegativities of O that is bonded to H this phenomenon also occurs when other highly electronegative elements, namely F and N, are bonded to H.

## Work/energy problem with friction

The more electronegative oxygen atom draws electron density, creating a net negative region in the molecule. This leaves the hydrogens electron-deficient, so they constitute a net postive region. In a bulk sample, negative ends of water molecules attract and align with the positive ends of their neighbors, creating a highly structured environment.

A large amount of energy 44 kJ per mole is required to disrupt these so-called hydrogen bonds, freely sendng water from the liquid to gaseous state. Prior to the onset of unrestricted phase change which we call boilingthe input heat energy is distributed in the liquid by increasing the rotations, vibrations, and mainly the translation of individual water molecules.

Because so many of these storage modes are available, water is a very effective temperature regulator taking in huge quantities of heat with small temperature changeand is therefore essential to temperature control in processes as diverse as internal combustion engines and climate systems.

The vast amount of water on Earth limits the daytime temperature changes to roughly a maximum of 20 oC, in spite of the planet's massive solar energy exposure. At night, the opposite process occurs; the heat energy stored by Earth's oceans is slowly released into the atmosphere to keep temperatures relatively stable without the presence of sunlight. Contrast this to the Moon, which is the same distance as Earth from the Sun, but is devoid of bodies of water. Temperature changes from night to day vary as much as several hundred oC.

If such large quantities of water were not present, it is hard to discern what impact such drastically varying temperatures would have had on the development of life on Earth. Heat energy is symbolized by q.

There is an important sign convention assigned to q to differentiate between the input or removal of heat.

### Thermodynamics Part 1: Work, Heat, Internal Energy and Enthalpy

When q is negative, a system is losing heat energy. This process is called exothermic. When q is positive, energy is input into the system and the process is called endothermic. Systems in thermal contact with their surroundings are able to exchange heat energy. Energetic changes in the surroundings result from thermochemical processes in the system, according to the First Law's conservation of energy. Heat exchange is measured in the system using the relation: Because m and S.

This formula also shows that a given amount of heat energy will cause a temperature change that is inversely proportional to the mass of sample. For example, consider the input of J of heat into each of three copper blocks with the following masses: The blocks will experience temperature changes of: Note that inputting heat implies a positive sign to the energy.

The above example shows that doubling the mass of material cuts its temperature change by one-half. Consider next the removal of 1. Because of the differences in their respective heat capacities, each will experience a different temperature change: Note that removal of heat implies a negative q value, and that for proper dimensional analysis, q must be expressed in J.

The final temperature is found according to the relationship: Supposing that all three are intially at a room temperature of Suppose now that a g block of iron heated to In accordance with the first law: If the system is perfectly insulated, the two blocks would remain at Tf for eternity.

By substituting the heat capacity formula, we can solve for this equilibrium temperature: Two isolated metal blocks under the given conditions would come to an equilbrium temperature of Schematic Diagram of a Bomb Calorimeter Naphthalene is a hydrocarbon often used in moth balls Calorimetry The science of calorimetry is used to determine the heat energy or caloric content of a material in familiar applications, the energy content of foods.

Using a device called a bomb calorimeter, a sample is placed in a chamber known as a bomb of known heat capacity which is immersed in water. The water bath is insulated to prevent heat loss to the outside.

Oxygen is pumped into the chamber, and a spark is used to ignite the sample. After complete combustion, the temperature inside the calorimeter reaches a maximum and this can be used to compute the heat energy content of the sample.

Traditionally, the calorie energy unit is used and is defined to be the amount of energy required to raise one gram of water one degree Celsius. Considering the calorimeter as an isolated system, the heat content of a sample burned in the bomb can be found from: The calorimeter chamber is filled with g of water and the initial temperature is measured at The bomb is ignited and the final temperature inside the calorimeter rises to a maximum of The heat content of the combustion reaction is found to be: Note that the combustion reaction is exothermic.

Using a molar mass of But you could do this on your own. So this is equal toand the sine of 5 degrees is 0. So when you multiply these out, what do I get? I'm using the calculator on Google actually.

So this is equal to So the height of the hill is So going back to the potential energy, we have the mass times the acceleration of gravity times the height. And this is equal to, and then I can use just my regular calculator since I don't have to figure out trig functions anymore. So so you can see the whole thing-- times 9. So this is equal to 38, joules or newton meters. And that's a lot of potential energy. At the bottom of the hill-- sorry, I have to readjust my chair-- at the bottom of the hill, all of this gets converted to, or maybe I should pose that as a question. Does all of it get converted to kinetic energy? We have a force of friction here. And friction, you can kind of view friction as something that eats up mechanical energy. These are also called nonconservative forces because when you have these forces at play, all of the force is not conserved. So a way to think about it is, is that the energy, let's just call it total energy.

So let's say total energy initial, well let me just write initial energy is equal to the energy wasted in friction-- I should have written just letters-- from friction plus final energy. So we know what the initial energy is in this system. And now let's figure out the energy wasted from friction, and the energy wasted from friction is the negative work that friction does.

And what does negative work mean? Well the bicyclist is moving meters in this direction. So distance is meters. But friction isn't acting along the same direction as distance. The whole time, friction is acting against the distance.

So when the force is going in the opposite direction as the distance, your work is negative.

Work Energy Theorem - Kinetic Energy, Work, Force, Displacement, Acceleration, Kinematics & Physics

So another way of thinking of this problem is energy initial is equal to, or you could say the energy initial plus the negative work of friction, right?

If we say that this is a negative quantity, then this is equal to the final energy. And here, I took the friction and put it on the other side because I said this is going to be a negative quantity in the system. And so you should always just make sure that if you have friction in the system, just as a reality check, that your final energy is less than your initial energy. Our initial energy is, let's just say What is the negative work that friction is doing?

Well it's meters. And the entire meters, it's always pushing back on the rider with a force of 60 newtons. So force times distance. So it's minus 60 newtons, cause it's going in the opposite direction of the motion, times And this is going to equal the ending, oh, no. This is going to equal the final energy, right?

## What are energy and work?

And what is this? So let's subtract 30, from 38, I didn't have to do that. I could have done that in my head. So that gives us 8, joules is equal to the final energy. And what is all the final energy? Well by this time, the rider's gotten back to, I guess we could call the sea level. So all of the energy is now going to be kinetic energy, right? What's the formula for kinetic energy? And we know what m is. The mass of the rider is So we have this is So if we divide both sides. So 8, divided by So we get v squared is equal to And let's take the square root of that and we get the velocity, So if we take the square root of both sides of this, so the final velocity is I know you can't read that.

And this was a slightly more interesting problem because here we had the energy wasn't completely conserved. Some of the energy, you could say, was eaten by friction. And actually that energy just didn't disappear into a vacuum.