Diesel cycle

Diesel cycle : The shaded area shows the net work done by the gas in the engine. The bigger the area the more work is done by the gas that will get your car moving.pic taken from PESwiki

RMS speed of molecules

Let c represent the rms speed of molecules.(Click to see animation)
KE = 1/2 m(square of c)
= 3/2kT
Starting from this single molecule 's kinetic energy relationship with temperature , you can derive the other relationship easily. Note :m is mass of a single molecule, if Nm =M (mass of the gas )
Internal energy U = 3/2 NkT ( which is kinetic energy of all the molecules )
This is only true for ideal gas , as for real gas Internal energy consists of sum of kinetic energy and potential energy of all the molecules.
If you relate to ideal gas law , pV= nRT which can also be written as pV= NkT .
The internal energy of the container of gas is also U=3/2 nRT or U= 3/2 pV.
This formula U=3/2 NkT helps you to understand why first law of thermodynamics uses this fact that increase in internal energy is proportional to the increase in temperature.

KE = 3/2 kT or 1/2 m(square of c)
Apply this formula:
If a container has different types of gas , which also mean they have the same temperture since the molecules exist together. They all have the same KE , therefore a molcules with twice the mass will only have c/(square root 2).

If a container having the same type of molecules , has its temperature raise to twice its initial temperature , then its speed would increase to (square root 2) c .

It is advised that you use the equation and write it twice, one for each case mentioned. Avoid using proportionality and memorising it. This will prevent overlooking some important. information.

First law of thermodynamics

Putting the first law of thermodynamics together involves you going to get information at the correct places.
1. work done = area under pv graph
W = + area(if process shows contraction)
W= -area(if process shows expansion)
2. increase internal energy proportional to temperature rise
positive if temperature rise and negative for temperature drop
3. heat supplied
positive if heat is absorbed and negative for heat released.

Putting 1,2 and 3 together means: increase in internal energy is equal to heat supplied and work done on the system.
Heat supplied cannot be seen from the pV graph . Increase in internal energy and work done can be deduced from the pV graph , from area and temperature change.
Common deductions:
1. If process end up with the same temperature, increase in internal energy =0. Also known as isothermal process.
2. If process does not show changes in volume , work done =0.Also known as isovolumic process.
3. If the process occurs in an system that is insulated , heat supplied =0 (no heat enter or leave the gas), also known as adiabatic process.


In obtaining these three information you have to look for Work and increase in internal energy from the pV graph using two equations w=p (V2-V1) and change in U= 1.5 nR(change in T) . Heat supplied cannot be found in the pV graph but in the question itself or a value to be found!
Finally check the + or - sign of each of the quanities before applying the first law of thermodynamics.

PV graphs

P,V,T graphs are 3D graphs that looks like the surface shown. For a fixed mass of gas, the possible P,V,T lies on the surface. The surface may be represented by the pV graph plus lines representing temperatures called isothermals ( constant temperature curves) It would be easier to figure out where you should draw a point leading to a higher temperature. Imagine if I give you a map without contours showing the height above sea level , you could underestimate the time you need to travel from one point to the next point without knowing whether it is uphill. Therefore, always draw faint lines to indicate isothermals so that you can draw your processes with arrows going in the right direction in case there is increase or decrease in temperature.