**Thermodynamics:**

- Thermodynamics is a branch of physics which deals with the inter-conversion between heat energy and any other form of energy.

**Thermodynamic State:**

- The simplest example of a system to which thermodynamics can be applied is a single chemically defined homogeneous substance.
- In this case, the thermodynamic state can be described completely by specifying any two of the three quantities, pressure P, volume V, and temperature T. These quantities are known as thermodynamic parameters or thermodynamic variables of the system.
- For a given amount of the substance forming the system, these three quantities are not independent. They are connected by a relationship of the general form which is called equation of state.
- It is for this reason that any two of these quantities are sufficient to describe the thermodynamic state completely. The two quantities are then called the thermodynamic coordinates.

**Terminology:**

**System:**

- The specified portion of the physical universe under thermodynamic study is called the system.
- e.g. A gas enclosed in a cylinder fitted with a piston is a system.

**Surroundings:**

- Remaining part of the universe outside the system which can exchange energy with the system and which change the properties of the system is called a surrounding.

**Universe:**

- The system and its surroundings are together known as the universe.

**Boundary:**

- The real or imaginary surface separating the system from the surrounding is called the boundary

**Isolated system:**

- A system which can exchange neither matter nor energy with the surroundings is called isolated system.
**Example:**A liquid placed in a thermos flask is an isolated system. Temperature change outside the flask does not change the temperature of the liquid. (no energy transfer) and nothing can escape from or enter the flask (no transfer of matter). The total amount of energy remains constant. Both the mass and temperature of the system constant.

**Homogeneous system:**

- When a system is a uniform throughout or consists of a single phase, it is said to be the homogeneous system.
**Example:**A pure single solid, liquid or a gas. A mixture of gases.

**Heterogeneous system:**

- A heterogeneous system is one which is not uniform throughout and which contains two or more phases which are separated from one another by definite boundary surface.
**Example:**Two immiscible liquids such as benzene and water

**Mechanical Equilibrium:**

- A thermodynamic system is said to be in mechanical equilibrium if no unbalanced forces and torques act between the system and the surroundings or between different parts of the system.

**Thermal Equilibrium:**

- A thermodynamic system is said to be in thermal equilibrium if the temperature of the system is the same throughout and the temperature of the system and the surroundings is the same.

**Chemical Equilibrium:**

- A thermodynamic system is said to be in chemical equilibrium if the chemical composition of the system is the same throughout.

**Thermodynamic Equilibrium:**

- A thermodynamic system is said to be in thermodynamic equilibrium if it is in mechanical, thermal and chemical equilibrium at the same time.

**Equation** **of** **a State:**

- The equation of state for any substance is a mathematical formula which expresses the relationship between the volume, pressure and temperature of the substance in any state of aggregation. Thus, for example, the equation of state for one mole a perfect gas is PV = RT
- The equation of the state can be written in the form, f(P, V, T) = 0.
- The thermodynamic state of the system can be specified by stating the values of two coordinates. The value of the third variable can be determined by using the equation of state of the system.

**Isothermal Process:**

- A process carried out at a constant temperature throughout the process is called isothermal process.

**Isothermal Change:**

- When a thermodynamic system undergoes a change in its state at a constant temperature, the change is said to be Isothermal change. The condition of Isothermal change is given by dT = 0.

**Conditions for Isothermal change:**

- The isothermal change can take place when the system is contained in a container having perfectly conducting walls due to which heat produced or absorbed during the change will flow out or flow in from the surrounding. Therefore, the temperature of the system remains constant.
- In practice, no perfect container is available and therefore perfect occurrence of isothermal change is impossible. However, a fairly approximate isothermal change is obtained when the change is made slowly.

**Examples of Isothermal Changes:**

- Ice is converted into the water at constant temperature.
- Water is converted into vapours at constant temperature i.e. boiling point of water.
- In Boyle’s law, gas can be allowed to expand or is compressed isothermally by changing the pressure on it.

**Isothermals or Isotherm or Isothermal Curves:**

- A graph of pressure versus volume at constant temperature is called isotherm or isothermal or isothermal curve. D
- A graph is drawn by taking pressure on the y-axis and volume on the x-axis. This graph is known as PV diagram or indicator diagram.
- Consider a gas occupying a volume v1 at pressure P
_{1}. The thermodynamic state of the gas is represented by a point H on the graph. Let us suppose that the gas undergoes an isothermal expansion from H to K along curve HK. Obviously, V_{2}> V_{1}. During expansion, the gas does an external work and its internal energy decreases. The curve HK is known as Isothermal curve or Isothermal.

- However, the change is made from K to H along curve KH, the gas undergoes an isothermal compression. Therefore, the volume of the gas decreases from V
_{2}to V_{1}. The external work is on the gas hence its internal energy increases. - For one mole of a perfect gas PV = RT or PV = constant. This relation at constant temperature is known as isothermal relation for a perfect gas.

**Phase:**

- The phase of a substance is defined as its form which is homogeneous, physically distinct and mechanically separable from other forms of the substance.
- The term phase as used in thermodynamics refers to the fact that the matter exists either as a solid, liquid or gas. If we consider the example of water, it exists in the solid phase as ice, in the liquid phase as water and in the gaseous phase as vapour. All the substances can exist in any of the three phases under proper conditions of temperature and pressure.

**Change of Phase:**

- The transitions from one phase to another takes place by the absorption or liberation of heat and usually by a change in volume and at a constant temperature.
- The temperature at which a phase change occurs also depends on pressure.

**Phase Diagram:**

- The phase diagram is the graph drawn in which pressure is represented along y-axis and temperature is represented on the x-axis.

- Phase diagram give the relationship between the phase in equilibrium in a system as a function of temperature, pressure and compositions. Phase diagrams are also known as Equilibrium diagrams or Constitutional diagrams.
- A phase diagram indicates the temperature at which the solid will start and finish melting and the possible phase changes which will occur as a result of altering the composition or temperature.
- The common point, where three lines of phases intersect is known as the triple point. At this point, the substance co-exists in equilibrium in all the three phases i.e. solid, liquid and vapour.

**Characteristics of Phase Diagram:**

- Different phases of a substance can be shown in a phase diagram.
- A region on a phase diagram represents a single phase of the substance, a curve represents an equilibrium between two phases and a common point represents an equilibrium between three phases.
- A phase diagram helps to determine the condition under which the different phases are in equilibrium.
- A phase diagram is useful for finding a convenient way in which desired change in phase can be produced

**Phase Diagram for Water:**

- Phase diagram of water consists of three curves sublimation curve, evaporation curve and melting curve meeting each other at a point called triple point. Due to these curves, the phase diagram has three regions
- The region to the left of melting curve and above the sublimation curve represents the solid phase of water i.e. ice. The region to the right of melting curve and above the evaporation curve represents the liquid phase of water i.e. water. The region below sublimation curve and evaporation curve represent the gaseous phase of water i.e. vapours.
- A curve on the phase diagram represents the boundary between two phases of the two substance. Along any curve, the two phases can coexist in equilibrium.
- Along melting curve, ice and water can remain in equilibrium. This curve is called fusion curve or ice line. This curve indicates that the melting point of ice decreases with increase in pressure.
- Along evaporation curve, water vapours and water can remain in equilibrium. This curve is called vaporisation curve or steam line. This curve indicates that the boiling point of water increases with increase in pressure.
- Along sublimation curve, ice and water vapours can remain in equilibrium. This curve is called sublimation line or hoar frost line.
- The three curves meet each other at a single point at A. This common point is known as the triple point of water. At the triple point of water can coexist in all the three states in equilibrium. The triple point of water corresponds to a pressure of 0.006023 atmospheres and temperature (0.01 °C) 273.16 K.

** ****Significance of Triple Point of Water: **

- Triple point temperature of the water is that temperature at which water can coexist in all the three states viz. Ice (solid), water (liquid), vapours (gas) in equilibrium.
- This triple point temperature of the water is used for defining absolute temperature scale. In absolute or Kelvin scale 0 K is considered as the lower fixed point while triple point temperature of the water is taken as the upper fixed point.
- Thus one kelvin temperature corresponds to 1/273.16 of the triple point temperature.

**Ideal Gas Equation:**

- The equation of state for an ideal gas is given by

PV = n RT

Where, P = Pressure of gas, V = Volume of gas, n = No. of moles of gas

R = Universal gas constant, T = Absolute temperature of gas.

For one mole of gas, PV = RT

**Van Der Wall’s Correction to Ideal Gas Equation:**

**Necessity of Correction of Ideal Gas Equation:**

- While deriving the ideal gas equation PV = RT, we had assumed that
- The volume occupied by the gas molecules themselves is negligible compared with total volume of the gas, and
- The molecules exert no appreciable force on one another.

- Both of these assumptions cannot be true at high pressure. When the gas is at high pressure, it has a small volume and therefore volume actually occupied by an individual molecule of a gas cannot be neglected in comparison with the volume of the entire gas.
- Also, at high pressure, the molecules come closer, therefore considerable cohesive forces ‘will be acting on them. Thus at high pressure and low temperature, the real gases do not obey the above relation.
- While modifying the perfect gas equation, PV = RT, both these factors were considered by van der Waals.

**Correction** **for** **Volume:**

- Let us consider a container containing the gas. The gas molecules are like hard elastic spheres. Let us assume that ‘r’ is their radius. Thus the distance between two molecules cannot be less than ‘2r’. Thus the presence of one molecule in the container will reduce the space available for another molecule by amount

- Thus the space available for free motion of gas molecules is less than the actual volume of the gas. Therefore, the corrected volume is taken as (V – b).
- The correction term ‘b’ is called co-volume and is equal to four times the actual volume occupied by the molecules.

Where N_{0} is no. of molecules of gas in the container

**Correction** **for** **Intermolecular** **Attraction****:**

- Consider a molecule A in the interior, far from the boundary. It is surrounded by other molecules equally distributed in all directions. Due to the similar forces (cohesive forces) acting upon it, symmetrically, from all sides the net intermolecular force acting on it is zero.
- Now, let us consider another gas molecule B near a wall of the container as shown in the figure. The cohesive force on B is due to adjacent molecules and the adhesive force due to the attraction between atoms of the wall with which molecule collides. Due to this inward pull acts on molecule B. Thus there is a small inward pressure p in addition to observed pressure P. Therefore corrected pressure is (P + p).
- The inward pressure depends upon
- The number of molecules striking per unit area of the wall per unit time (p ∝ n) and
- The number of attracting molecules per unit volume which attract the colliding molecule. (p ∝ n). Both these factors are proportional to the density of the gas.

Thus, p ∝ n²

If N be the number of molecules present in volume V of the gas, then n = N / V

where ‘a’ is some constant and V is the volume of the gas. Therefore, corrected pressure ( P + p) becomes

Thus van der walls corrected equation for one mole of gas is

**Drawbacks of Van der wall’s Correction:**

- According to Van der walls, a and b are constants for given gas, but it is found that the constants a and b change in temperature.
- The shape of theoretical isotherm plotted using Van der walls equation is different from the experimentally drawn isotherm