Thermodynamics Formulas

Thermodynamics Formulas. The Steam engine is the first machine to be invented. It uses high-pressure steam to push a piston in a cylinder. The steam is produced by heating the water by using the flame from coal or gasoline. The Steam from the boiler is then delivered to a cylinder through a valve; this high-pressure steam will push the piston. When the piston is pushed to the edge of the cylinder through one edge and allows new steam pushes the piston back to its initial position. This cycle will keep on going as long as the steam is provided. The perpetual motion of the piston can be used to move another part of the engine.

Steam engine applies the concept of thermodynamics. And so do diesel engine, refrigerator, and air conditioner (AC); their working principles are the applications of thermodynamics concept.

Basic Concept Of Thermodynamics

Thermodynamics is a branch of physics that studies the relation of heat, mechanical energy, and its conversion from one into the other. Before studying thermodynamics, we first need to understand the definition of system and environment besides the terms of equilibrium, heat, work, and energy.

1. System and Environment

the system can be defined as a separated part which becomes the point of observation. A system can be a room, body, quantity of matter, etc. Environment or surroundings can be defined as anything outside the system which may influence the state of the system directly.

2. Equilibrium 

There is term "equilibrium" in thermodynamics. There are three types of equilibrium in thermodynamics, i.e. mechanical, chemical, and thermal equilibrium. when the conditions for the equilibrium to take place are fulfilled, then the system is said to be in a thermodynamic equilibrium. In that state, there is no tendency of state alteration in either system or its environment.

3. Definition of Heat

Heat is energy which moves due to the temperature difference between the system and its environment. The system can release heat to its environment, and on the contrary, the environment can also send out its heat to the system.

4. Definition of work thermodynamics

Figure 8.2 shows liquid in a cylinder equipped with a freely moving piston. If the cylinder's cross-section is A and the pressure given by the piston is P, then the force produces is F = PA. When the piston moves outward at a distance of dx, the work dW performed by the force F is:

dW = F dx = PA dx

However, A dx = dV or the volume change and so we have

dW = P dV

During the volume change from V₂ to V₁, the pressure P is constant as shown in Figure 8.3, and so the work performed by the system is

W = P(V₂ - V₁) 

Therefore, in every process with constant volume (V₁ = V₂), the work performed by the system in equal to zero. If V₂ > V₁ it means the work is performed by the system; its value is positive. Inversely, If V₂ > V₁, it means the work is given to the system; its value is negative.

Example :

A certain gas undergoes expansion at a constant pressure of 5 atm (1 atm = 10⁵ N/m²). Its initial volume was 300 L and the volume gets doubled soon after the expansion. Determine the work done by the gas.

Answer :

P = 5 atm = 5 x 10⁵ N/m²

V₁ = 300 L = 0,3 m³
V₂ = 2V₁ = (2) (0,3 m³ ) = 0,6 m³
W = P ΔV
 W =  P(V₂ - V₁)  = (5 x 10⁵ N/m²) ( 0,6 m³ - 0,3 m³) = 1,5 x 10⁵ J

Internal Energy

Every particle in a system always moves. Given that kinetic energy of each particle in a system is E_k, and the total number of particle in the system is N, the internal energy (U) of the system can then be expressed by:

U = NE_k

Internal energy is conservative; meaning that its value does not depend on the path or process was taken; it depends only on the initial and the final state of the system. Internal energy is a characterized state of gas which can not be measured directly. The thing that can be measured directly is the change of internal energy (ΔU); it is when the system changes from its initial state (U₁) to its final state (U₂). Internal energy is a state function which the change is formulated by 

ΔU = U₂ - U₁

 Thermodynamic Process

Process or the change of thermodynamic state can be classified into two, i.e irreversible and reversible processes. The irreversible process is a spontaneous process in one direction; it can not occur in the reverse direction. The reversible process is a process of which the direction can be reversed. The reversible process is an equilibrium process. The system that undergoes a reversible process will always be in a state of thermodynamic equilibrium.

The thermodynamic process can be in the form of expansion, compression, heating, or cooling processes. The thermodynamic process can take place in a state of isothermal, Isochoric, isobaric, or adiabatic processes.

1. Isothermal

An isothermal process is a process of state alteration of gas which takes place at constant temperature.

This process agrees with Boyle's law, which states that the value of PV is constant at a fixed temperature or more clearly stated by the general equation of ideal gas, PV= nRT. The work performed received by the system can be obtained by calculating the area under the P-V curve.

In fact, the work W in the equation above has the same meaning with the area below the curve on P-V graph. Suppose you have learned the integral concept as the area below the curve of a function, you certainly understand that formulation.

2. Isochoric

Icochoric process is a process of the state alteration of gas which takes place at constant volume.

 Isochoric process agrees with Charles' law, which states that the value of P/T is constant at a fixed volume. What is the value of work in the isochoric process? By remembering the work definition as the area below the curve of P-V graph, you can conclude that the work in isochoric process is zero (W=0). It can also be understood that there is no volume change, therefore we have ΔV = 0, W = ΔV = 0.

3. Isobaric

Isobaric process is a process of gas state alteration which takes places at a constant pressure.

Isobaric process agrees with Gay-Lussac's law, which states that the value of V/T is constant for a fixed pressure. How much work is involved in the isobaric process? By noticing the curve of P-V graph, you can determine the value of the work as an area below it.
W = P(V₂ – V₁) = P ΔV
The process of gas state alteration of gas state alteration in a steam engine's boiler is usually isobaric. The steam volume addition process in the boiler is carried out without changing the pressure inside it.

Thermodynamics Eequation

1)  A thermodynamics process without any heat transfer between the system and its surroundings is called........
a.  Adiabatic
b.  Isochoric
c.  Isobaric
d.  Isothermal
e.  Isovolume

2) An amount of 2 x 10^-3  mol gas expands isothermally from V₁ = 20 cm³ to V₂ = 50 cm³ at the temperature of T = 300 K. If the universal gas constant is R = 8.3 J/mol.K, the work performed in the system is..........
a.  4.56 x 10³ Joule
b.  4.56 x 10² Joule
c.  4.56 x 10¹ Joule
d.  0.456 x 10^-1 Joule
e.  0.456  Joule

3) A kind of gas in a cylinder has an initial volume of  20 cm³. The gas experiences expansion at a constant pressure of 2 x 10⁴ N/m² in a way that its volume becomes 40 cm³; the work performed is.....
a.  0.2 Joule
b.  0.3 Joule
c.   0.4 Joule
d.  0.5 Joule
e.  0.6 Joule

4) An amount of 1.5 m³ helium gas at a temperature of 27^oC is heated isobarically to 87^oC. If the pressure of the helium gas is 2 x 10⁵ N/m², its external work will be .........
a.  60 kJ
b.  120 kJ
c.  280 kJ
d.  480 kJ
e.  660 kJ

5)  A mol of ideal gas at a temperature of T is in a cylinder equipped with the frictionless piston. The gas is then heated at constant pressure in a way that its volume becomes fourth of its initial. If R is the universal gas constant, the work performed by the gas is..........
a.   RT/4
b.   RT ln 4
c.   6RT
d.   4RT
e.   3RT

You Need To Know

Refrigerator in an electronic appliance we find regularly in our everyday life. The working principle of the refrigerator is making use of the second law of thermodynamics. The room inside the refrigerator acts as a cold reservoir whose temperature is  T_C, whereas the room outside the refrigerator act as the hot reservoir whose temperature is Th,

The heat in the cold reservoir is generated by the foods, drinks, or other things in the refrigerator. This heat will be removed and delivered to the outside air around the refrigerator. The electric energy is needed to flow the heat from the cold reservoir to the hot one. The electric energy used to operate the refrigerator is provider by our household electric installation. We buy this electric energy from a provider. In order to save the electric cost, it is necessary for us to chose the high effectiveness refrigerator.

inernal energy Thermodynamics

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