A change in pressure and volume of a gas without any change in its temperature is called an isothermal change. In such a change, there is free exchange of heat between the gas and its surrounding. These changes are governed by Boyle's law i.e., PV = Constant. The change in pressure and volume of a gas when temperature also changes is called an adiabatic change. In such a change, no heat is allowed to enter into or escape from the gas. The equation of adiabatic changes \(P V^{\gamma}\) = constant or \(T V^{\gamma-1}\) constant or \(P^{1-\gamma} T^{\gamma}\) = constant, where \(\gamma\) - ratio of two principal specific heats of the gas = \(\frac{C_{P}}{C_{V}}\) .
(i) What are conditions for the changes to be isothermal and for adiabatic?
(ii) A gas is compressed isothermally to half its volume. By what factor does the pressure of the gas increase? 
Given \(\gamma\) = 1.4.
(iii) A gas is compressed adiabatically to half its volume. By what factor does the pressure of gas increases? 
Given \(\gamma\) = 1.4.
(iv) A gas is suddenly compressed to \(\frac{1}{4}\)th of its original 4 volume. Calculate the rise in temperature, when the original temperature is 27°C and  \(\gamma\) = 1.5.
(v) Draw PV variation diagram representing isothermal and adiabatic processes respectively.
(vi) Ice at 0 °C is converted into steam at 100°C. State the isothermal changes in this process

Thermodynamics is the study of transformation of heat into other forms of energy and vice-versa. Thermodynamical system is said to be in equilibrium when macroscopic variables like pressure, volume, temperature, mass, composition, etc. that characterise the system variables which are not necessarily independent. Some important thermodynamic processes are: isothermal, adiabatic, isobaric, and isochoric. A thermodynamic state is represented by equation of state that represents the connection between the state variables of a system.
(i) Which physical quantity determine the thermal equilibrium of a system? State zeroth law of thermodynamics.
(ii) What is quasi static process? What does it represent? 
(iii) What is equation of state? Write equation of state for adiabatic operation.
(iv) Determine the specific heat of gas during isothermal and adiabatic process.
(v) The volume of an ideal gas is Vat a pressure P. On increasing the pressure by \(\Delta \boldsymbol{P}\) , the change in volume of the gas is \(\Delta \boldsymbol{V}_{\mathbf{1}}\) under isothermal conditions and \(\Delta \boldsymbol{V}_{2}\) under adiabatic condition. Is \(\Delta V_{1}>\Delta V_{2}\) or vice versa and why?
(vi) An ideal gas at temperature T_1, undergoes expansion under adiabatic conditions, to attain temperature T_2. Write expression for workdone.

Every system (solid, liquid or gas) possess a certain amount of energy. This energy is called the internal energy and is consists of two parts
(i) Kinetic energy due to the motion (translation, rotational, and vibrational) of the molecules and
(ii) potential energy due to the configuration (separation) of the molecules. The internal energy of a homogeneous system depends on its thermodynamic state i.e., on its thermodynamic coordinates P, V, and T. Each definite state of the system possesses a definite quantity of internal energy. A change in the internal energy can occur only if a transfer of energy between the system and surrounding is permitted. This can take place if some work is performed on or by the system and some heat is absorbed or given out by the system.
(i) How temperature, pressure and volume of gas change in an isothermal process?
(ii) 200 J of work is done on a gas to reduce its volume by compressing it. If this change is done under adiabatic conditions. Find the change in internal energy of the gas and also the amount of heat absorbed by the gas?
(iii) In a given process on an ideal gas dW = 0 and dQ >0, then what change would occur in temperature and internal energy?
(iv) What are two different modes of changing state of a thermodynamic system?
(v) Write the sign convention regarding to change in heat content, internal energy change and work done over a thermodynamic system during a thermodynamic process.
(vi) What will be the change in internal energy during isothermal, adiabatic and cyclic process?

The first law of thermodynamics establishes the essential equivalence between work and heat, as according to this law, internal energy (and hence temperature) of a system can be increased either by supplying heat to it or by doing work on the system or both. However, this law has limitations as it does not indicate the direction in which the change can occur and gives no idea about the extent of change. Limitations of first law of thermodynamics is overcome by second law of thermodynamics expressed as Kelvin Planck statement and Clausius statement based on working of heat engine and refrigerator respectively.
(i) Write the relation between two principal specific heats of an ideal gas based on first law of thermodynamics.
(ii) Which fundamental law of conservation is represented by first law of thermodynamics?
(iii) State Kelvin Planck statement and Claus statement of second law of thermodynamics.
(iv) Define thermal efficiency of a heat engine.
(v) Define coefficient of performance of a refrigerator \(\text { ( } \beta \text { ) }\).State the relation between \(\eta \text { and } {\beta}\) .
(vi) Can a heat engine of 100% efficiency be designed? Explain.

A sample of2 kg of mono atomic helium is taken through the process ABC and another sample of 2 kg of the same gas is taken through the process ADC as shown in diagram. The molecular mass of Helium = 4 and R (gas constant) = 8.3 JK^-1 mol^-1.

(i) If number of moles of helium being 500, then Determine the temperature of State A.
(ii) What is isochoric process? Determine the temperature at state B.
(iii) What is isobaric process? Determine the temperature at state C and D.
(iv) Determine the work done in process ABC.