MHT-CET : Physics Entrance Exam

### MHT - CET : Physics - Thermodynamics Page 1

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 1. System Any quantity of matter, which contains large number of molecules or particles bounded by a closed surface, is termed as a system.

 2. Surroundings Everything outside the system that is capable of exchanging energy with the system is known as its surroundings.

 3. Isolated System A system that cannot exchange matter or energy with the surroundings is an isolated system.

 4. Open System A system that can exchange both matter and energy with the surroundings is an open system.

 5. Closed System A system that can exchange only energy with the surroundings is a closed system.

 6. Homogeneous and Heterogeneous System A system, which is completely uniform throughout, is said to be homogeneous while a system that is not uniform throughout is said to be a heterogeneous system.

 7. Thermal Equilibrium A system is said to be under thermal equilibrium if its temperature is the same in all parts of the system and is equal to the temperature of the surroundings.

 8. Mechanical Equilibrium A system is said to be under mechanical equilibrium if no unbalanced force is acting on any part of the system.

 9. Chemical Equilibrium A system is said be in chemical equilibrium if its chemical composition does not change with time.

 10. Thermodynamic Equilibrium A system in which its observable properties like composition, pressure, volume and temperature do not change with time is said to be in thermodynamic equilibrium.

 11. Thermodynamic State A system, which is in thermal equilibrium, can be described completely by specifying its thermodynamic co-ordinates such as pressure P, volume V and temperature T. The state described by these thermodynamic co-ordinates is called the thermodynamic state of the system. Note: The thermodynamic variables are not totally independent, they are inter-related. Out of the three co-ordinates (P, V, T), any two are sufficient to specify the state of the system.

 12. Equation of State The relation concerning pressure, volume and absolute temperature of a substance is known as the Equation of State of that substance. If P, V, T denote pressure, volume and temperature of a system, then f (P, V, T) = 0 is an equation of state. The equation of state of a system Depends upon the characteristic property of the system. Holds good over certain range of temperature. Equation of State for a perfect gas PV = nRT Where n: number of moles of the gas R: universal gas constant For n = 1, PV = RT

13.

Isothermals

Isothermal Change: When a thermodynamic system undergoes a change in its state at constant temperature, the change is said to be an isothermal change.

The process in which the temperature of the system remains constant is an isothermal process.
e.g. Melting or boiling of a substance.

In an isothermal change:

• The temperature of the system is constant.
• The change is a slow process.
• Heat is absorbed or released during the process.
• The internal energy of the system remains constant.
• The heat absorbed or released is used or got from the external work done on/by the system.
dQ = dW

An isothermal is a curve which graphically represents the relation between pressure and volume of a gas at constant temperature.

With the help of an isothermal or isotherm, the work done in expansion is determined to be

W = RT loge

 V2 V1

 where V1: initial volume V2: final volume

...P1V1 = P2V2,       W = RT loge

 P1 P2

 14. Phases The phase of a substance is defined as the form of the substance which is chemically homogeneous, physically distinct and mechanically separable from other forms of the same substance. Example: The three states of a substance - solid, liquid and gaseous - are the phases of a substance. Phase diagram: It is a graph representing the variation of pressure (P) with temperature (T) of the substance. The different phases of a substance can be represented by a phase diagram.

Phase diagram of water

 A: Triple point of water AB: Fusion curve AC: Vaporisation curve AD: Sublimation curve

The curves divide the phase diagram into three regions, each corresponding to a definite phase of water.

 AB: Fusion curve - Curve of co-existence of solid and liquid phases. Ice and water remain in equilibrium along AB. AC: Vaporisation curve - Curve of co-existence of solid and vapour phases. Water and water vapour remain in equilibrium along AC. AD: Sublimation curve - Curve of co-existence of solid and vapour phases. Water vapour and ice remain in equilibrium along AD. A: Point of intersection of the three curves - Triple point of water.

It represents the unique condition in which all the three phases of water co-exist in equilibrium.

In case of water, the temperature corresponding to the triple point is taken as 273.16 K.

Significance of triple point of water

·

Its value is fixed at 273.16 K

·

In Kelvin's absolute scale, O°K is the lower fixed point while the triple point of water is the upper fixed point.

·

The interval between the two fixed points is divided into 273.16 equal parts and each part is considered as 1K.

·

1K is the fraction

 1 273.16

of the temperature of triple point of water.

Importance of phase diagram

 · It enables the determination of the conditions under which different phases are in equilibrium. · It is useful in determination of the phase change of a substance. · It is used to determine the triple point of a substance. · It is useful in understanding the P-T relationship for a substance.

15.

Van der Waals' Equation of State

• Equation of state for one mole of an ideal gas
PV = RT
• The ideal gas equation is based on the assumptions of the kinetic theory of gases:
1. The volume of the gas molecules is negligible compared to the total volume of the gas
2. The forces of attraction between the gas molecules are negligible.
• These assumptions are not true at high pressures and low temperatures. The ideal gas equation was modified by Van der Waals.
• The corrections introduced by Van der Waals.
1. Finite volume of gas molecules.
2. Pressure of the gas.

• Inward pressure due to molecules: p
p
a n2, n: number of molecules per unit volume of gas

n =

 N V

N: total number of molecules

V: volume of gas

\ p a

 N2 V2

, p a

 1 V2

(N = constant)

\ p =

 a V2

where a is a constant

\ Corrected pressure P + p = P +

 a V2

•
• Corrected volume = V - b      (b is a constant for a given gas.)
Due to finite volume of molecules, space available for free motion of molecules is less than the actual volume V of the container.

Reduction in volume due to finite molecular size

=

 4 3

p (2r)3 where 2r = molecular diameter.

•
• \ Van der Waals' equation of state for real gas

(P +

 a V2

) (V - b) = RT

• a, b are Van der Waals' constants.

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