The following equation describes SPECIFIC HEAT CAPACITY.
Where,
Q= Heat supplied to substance,
m= Mass of the substance,
c= Specific heat capacity,
T= Temperature rise.
Enthalpy
Enthalpy is a measure of heat and energy in the system. Scientists figure out the mass of a substance when it is under a constant pressure. Once they figure out the mass, they measure the internal energy of the system. All together, that energy is the enthalpy. They use the formula "H = U + PV." H is the enthalpy value, U is the amount of internal energy, and P and V are Pressure and Volume of the system. This system works really well for gases.
There are things that affect the level of enthalpy in a system. The enthalpy is directly proportional to the amount of substance you have. Chances are if you have more of a substance, you have more energy. More energy means higher enthalpy.
Another thing to remember is that the value for H (enthalpy) changes sign when the reactions or values are reversed. When a reaction moves in one direction, the sign is positive. When a reaction is moves in the opposite direction, the value is negative.
Finally we have Hess's law. If a process happens in stages or steps, then the enthalpic change for the overall system can be determined by adding the changes in enthalpy for each step.
Constants
ADIABATIC
This term describes a system that changes and there is no transfer of heat in or out. If a system expands ADIABATICALLY, then the internal energy of the system usually decreases. It's as if you have a cup of water just out of the tap. You let the cup sit and the water settles down. Less energy and no transfer of heat.
ISOVOLUMIC
You can probably see the word "VOLUM" in there. "ISO" usually stands for constant. Put them together and you get a system that changes, but the volume stays constant. These types of changes do not produce any work on the environment. The amount of energy changes, but the heat just stays inside the system.
ISOBARIC
You've seen the prefix "ISO," the suffix "BARIC" refers to pressure. This is a system that changes, but keeps a constant pressure. All of the change is in the volume of gas in the system. Like blowing up a rubber balloon.
ISOTHERMAL
One last "ISO" the suffix now is "THERMAL." Systems that change in every way but their temperature. You would say that these systems are in THERMAL EQUILIBRIUM. You can see that the pressure and volume change. The curve is like the adiabatic process, but there is no increase in temperature.
The equation of continuity
When trying to solve a problem we are told to look for things that stay the same. They then can be set equal to each other giving an equation to solve. Rules like that are easy to state, but examples are easier to understand.
If we have water flowing through a pipe filled with water, the water will enter at a certain rate and leave at the same rate. The quantity pushed in per unit time will push out an equal amount. That seems like an obvious and reasonable observation. What are we taking for granted in the argument? We are assuming that water is incompressible, and its flow is steady it does not speed up or slow down
Volume is expressed as cubic units, cubic feet, cubic centimeters and so forth. Time can easily be changed from hours to minutes or seconds. So the rate of flow could be expressed as cubic centimeters per second. Cubic cenimeters per second could also be expressed as square centimeters times centimeters per second. Square centimeters and centimeters per second are measures of Area and velocity, respectively. So the rate of flow could be expressed as volume per time equals area times velocity. The velocity would be an average velocity since we are using the total volume per unit time. The water in the center of the pipe goes faster than the water at the pipe wall. However the pipes have cross sectional areas and the water has an average velocity. So we could use the area of the entry or the exit opening. If we multiply the cross sectional area of the pipe (cm2) times the velocity of the water (cm / sec.) we get Cubic centimeters per second, volume per unit time, a rate of flow. It makes sense both ways. Does it matter what cross sections we use? If our principle that the quantity of matter flowing in, is the same as the amount flowing out then it must also be true everywhere in the pipe.
Therefore we can say that AV = K
Where A is cross sectional area at a point.
V is the average velocity for this point.
And K is a constant ‘the rate of flow in the pipe’.
Since the equation is true for any two points in the pipe we can say that :
A¹V¹ = A²V²
Where A¹V¹ is the area and velocity at one point in the pipe and A²V² is the area and velocity at another point.
This is called the continuity equation and it shows us that the velocity of water at a point in a full pipe is inversely proportional to the cross sectional area of the pipe
at that point. So if a pipe gets bigger the velocity in the pipe will decrease and vice versa.
Area at X is 10cm² and velocity is 1cm per second
Area at Y is 1cm² and velocity is 10 cm per second