Celsius, Farenheit and Kelvin Temperature Scales

 

Farenheit: water freezes at 320 F and boils at 2120 F

 

Celsius (Centigrade): water freezes at 00 C and boils at 1000 C

 

Convert F to C:   F = (9/5).C + 32

 

Convert C to F:   C = (5/9).(F – 32)

 

– 400 F = – 400 C

 

Kelvin (Absolute) temperature: zero temperature – 2730C

 

Convert C to K:   C = K + 273

 

Convert F to K:   F = (9/5)K – 459,4

 

Heat Capacity

 

Heat capacity tells us how much the temperature of an object will increase for a given amount of energy or heat input. It is deped as:

 

 

C – heat capacity;

Q – the heat;

T – the temperature;

 

Specific Heat

 

 

m – mass;

 

Molar Specific Heat

 

Instead of defining specific heat with the mass of the object, we could define it according to the total number of molecules in the object.

 

mole = 6,02 . 1023

 

Thus molar specific heat is defined as:

 

 

N – the number of moles of molecules in the substance.

 

A Closer Look at Heat and Work

 

When discussing work and energy for thermodynamic systems it is useful to think about compressing the gas in a piston, as shown in Fig. 1.

 

Fig 1

 

By pushing on the piston the gas is compressed, or if the gas is heated the piston expands. Such pistons are crucial to the operation of automobile engines. The gas consists of a mixture of gasoline which is compressed by the piston. Sitting inside the chamber is a spark plug which ignites the gas and pushes the piston out. The piston is connected to a crankshaft connecting the auto engine to the wheels of the automobile. Another such piston system is the simple bicycle pump. Recall our definition of Work as:

 

 

For the piston, all the motion occurs in 1-dimension so that

 

 

(or equivalently ). The pressure of a gas is defined as force divided by area (of the piston compressing the gas) or:

 

 

giving dW = pAdx = pdV where the volume is just area times distance or dV = Adx. That is when we compress the piston by a distance dx, the volume of the gas changes by dV = Adx where A is the cross-sectional area of the piston. Writing W = int(dW) gives:

 

 

which is the work done by a gas of pressure p changing its volume from Vi to Vf (or the work done on the gas).

 

The First Law of Thermodynamics

 

The first law of thermodynamics is nothing more than a re-statement of the work energy theorem, which was:

 

 

Recall that the total work W was always W = DK. Identify heat Q as Q = WNC and internal energy (such as energy stored in a gas, which is just potential energy) is Eint = U and we have DEint +W = Q or

 

DEint = Q – W

 

which is the first law of thermodynamics. The meaning of this law is that the internal energy of a system can be changed by adding heat or doing work. Often the first law is written for tiny changes as:

 

dEint = dQ – dW

 

Special Cases of 1st Law of Thermodynamics

 

Adiabatic Processes

Adiabatic processes are those that occur so rapidly that there is no transfer of heat between the system and its environment. Thus Q = 0 and

 

DEint = – W

 

For example if we push in the piston very quickly then our work will increase the internal energy of the gas. It will store potential energy (DU = DEint) like a spring and make the piston bounce back when we let it go.

 

Constant-volume Processes

 

If we glue the piston so that it won't move then obviously the volume is constant, and W = int (pdV) = 0, because the piston can't move. Thus:

 

DEint = Q

 

which means the only way to increase the internal energy of the gas is by adding heat Q.

 

Cyclical Processes

Recall the motion of a spring. It is a cyclical process in which the spring oscillates back and forth. After one complete cycle the potential energy U of the spring has not changed, thus DU = 0. Similarly we can push in the piston, then let it go and it will push back to where it started, similar to the spring. Thus DEint = 0 and Q = W meaning that work done equals heat gained.

 

Free Expansion

Another way to get DEint = 0 is for Q = W = 0