First Law of Thermodynamics Equations

A closed system can change the form of its energy with the help of its surroundings through work and heat transfer. Heat and work are the forms of energy that can be transferred around the system’s boundary and cause a similar effect on the system. The energy that enters the system as work may leave as heat and is also a reversible process.

The first law of thermodynamics states that during an interaction between a system and its surroundings, the amount of energy gained by the system must be exactly equal to the amount of energy lost by the surroundings. Now, we will talk about all the elements that affect the energy equation, such as heat, work and internal energy.

The First Law of Thermodynamic Equations

Heat transfer

Heat is a form of energy that is transferred between two different systems with the help of temperature differences. Keep in mind that there can not be any heat transfer between the system if they are at the same temperature.

The unit of heat is kJ or BTU. The amount of heat transferred is the rate of heat transferred per unit time. It is a vector quantity; therefore, it has magnitude, point of action and direction.

Modes of heat transfer

Heat can be transferred in three different modes:

• convection
• radiation
• conduction.

And all these modes require the existence of different temperatures.

Convection is the mode of heat transfer between a solid surface and the adjacent gas or liquid in motion. It is the combined effect of affection and conduction. Convection is also known as forced if the fluid present is forced in motion with the help of a pump. It is also called natural or free if the fluid present is in motion because of the buoyancy force.

Conduction is the transfer of force or energy caused by energetic particles to the adjacent less energetic particles due to interaction with both particles. In a solid matter, conduction will be caused because of the combination of vibrations of the particles in a lattice and energy transported by free particles.

Radiation: radiation is the type of energy released in the form of electromagnetic waves by matter or particles. This results in the change of electronic configurations of the molecules or the atom.

Heat

Heat is denoted with Q, and it is the energy transfer around the boundary of a system.

Work

Work is denoted with W, and there are different types of work transfer around the boundary of a system:

• Boundary work Wb piston or cylinder
• Electric Work We Volts.amps.time
• Shaft work Ws Paddlewheel

The boundary work is evaluated by integrating the force F and multiplying by the incremental distance mode dx between state 1 and state 2. When dealing with a piston-cylinder device, the force can be replaced by the area of piston A and multiplied by the pressure P, replacing Adx by a change in volume dV:

W_1-2=₁ ∫² F dx=₁ ∫² PAdx=₁ ∫² PdV

₁ ∫² PdV= (area under the curve)

If the mass of the system is m(kg) then we will get:

W_1-2=₁ ∫² P dV=m₁ ∫² P dv=mw_1-2

P = Pressure (kPa)

V = volume (m3)

m = Mass (kg)

v = specific volume (m3/kg)

W = work done (kJ)

w = Specific work done (kJ/kg)

Internal Energy (u)

The third part of the energy equation is the change in internal energy, which results in work or heat transfer. Specific internal energy is the property of the system.

Energy Equation for stationary closed system

Q-W=ΔU [kJ]

ΔU = change in energy

Q = Heat added

W= work done by the system

Now, divide each term of the equation with system mass m(kg). We will get the specific form of the equation:

q-w=Δu [kJ/kg]

Enthalpy (h)

It is one of the major parts of the equation.

Enthalpy [kJ]: H=U+PV

Specific Enthalpy [kJkg]:h=u+Pv

Now applying the energy equation obtained:

W_1-2=₁ ∫²PdV=P(V₂-V₂)

Substituting the values in energy equation and simplifying:

Q=U₂-U₁+P(V₂-V₂)=H₂-H₁

Q=ΔH (constant pressure process)

Conclusion

The first thermodynamic law is Q-W=ΔU, where ΔU is the change in energy, W is the work, and Q is the heat transferred. Both the heat transferred and the work done is energy in transit, and the internal energy U depends on the system’s state. Coming across all the above points has explained the first law of thermodynamics and its equations in detail.

It is a law through which you can understand the relationship between heat and work and the energy or internal energy. With the interaction between heat, energy and work, energy is transferred, and conversion is caused every time a change is made in the system. Note: no energy is created or lost during the transfer of energy.