Thermodynamics Formula is a subfield of physics that studies the interactions between internal energy, work, and heat transmission. In thermodynamics, the system is defined as a quantity of matter or a system in space under observation. The environment, often known as the surroundings, is everything outside of the system. The boundary line is the theoretical or physical line dividing the system from its surroundings.

Zeroth Law of Thermodynamics

As per Zeroth law of Thermodynamics, if two thermodynamic systems are in thermal equilibrium with the third system, then all three systems are in thermal equilibrium with each other. We can take the example of the thermometer which is based on Zeroth law.

First Law of Thermodynamics

The first law of thermodynamics defines that energy can neither be created nor destroyed, it can be only transformed from one form to another form.

Mathematically,      ΔQ =  ΔU +  ΔW

Here,  ΔQ is the heat supplied to the system,

           ΔU is the change in internal energy of the system,

           and ΔW is work done by the system.

Also, ΔW = PΔV, where P is pressure and ΔV is the change in the volume of the system.

Thus,   ΔQ =  ΔU +  PΔV

Also Check – Unit, Dimension & Vector Formula

Sign Conventions in Thermodynamics

Work done on the system = Negative

Work done by the system = Positive

Heat supplied or added to the system = Positive

Heat rejected or removed by the system = Negative

Download PDF Thermodynamic Formula

Work done in different Thermodynamic processes

Work done in isobaric (constant pressure) process, 

 W = PΔV 

Work done in isochoric (constant volume) process,

 W = PΔV = P *0 = 0 

Work done in isothermal( constant temperature) process,

W = -nRTln (V2/V1) = -2.303nRTlog(V2/V1)

 Here, n = number of moles of gas

           R = Gas constant 

           T = temperature of system

Work done in adiabatic process,

Also Check – Transmission of Heat Formula

Also, slope of adiabatic process = ( slope of the isothermal process)

Entropy 

Entropy is defined as a measure of randomness or disorder of a system.

Change in entropy of the system, ΔS = Q_rev*T 

Where Q_rev is the heat supplied reversibly and isothermally.

Second Law of Thermodynamics

The second law of thermodynamics can be stated as follows

Kelvin-Planck Statement: It is not possible to construct a machine which is working in a cycle has the sole effect of extracting heat from a single reservoir and performing a same amount of work.

Clausius Statement: It is impossible to design a machine that works on a cycle and produces no effect other than heat transfer from a cold body to a hot body.

Carnot Cycle 

Carnot cycle is a theoretical cycle that is an ideal reversible closed thermodynamic cycle. It consists of the following four processes:

Isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.

The theoretical engine based on this cycle is called as Carnot Engine and according to Carnot theorem, 

Any system working between a hot reservoir and a cold reservoir can never have higher efficiency than the Carnot engine operating between the same reservoirs. 

The efficiency of the Carnot Cycle is given by, 

                   = 1 -( T2/T1)                                 (T1 > T2)

Where T1 is the hot reservoir (source) temperature and T2 is the the sink temperature.

Heat Engine

A heat engine is a device that uses a heated source as a reservoir and transfers heat from there to perform work. There is a rejection of some heat to the sink (cold body).

The basic diagram of a heat engine is shown as, 

Here Q1 is the heat extracted from the 

hot reservoir and Q2 is the heat 

rejected to the the sink.

W is the work done by the heat engine.

Refrigerator 

It is basically a heat engine operated in the reverse direction.

The basic diagram is shown as

Work done on the system = W

Heat taken from sink = Q2

Heat rejected to reservoir = Q1

Now, Q1 = Q2 + W

Specific Heats

There are two specific heats, one is specific heat at constant volume (Cv) and specific heat at constant pressure (Cp)

Specific heat is that the quantity of heat essential to increase the temperature of 1 gram of any substance by 1 degree Centigrade.

Specific heat, C = Q*m*T’

Here, Q is heat gained or lost by the system.

T is the change in the temperature of the system.

Also Cp  is related to Cv by the relation, Cp – Cv= R, where R is the universal gas constant.