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State variable:- State functions are the fundamental properties which determine the state of a system. These are called state variables. A list of the state variables which describe the state of a system is given below: Pressure(p), Temperature(T), Volume(V), Internal energy(E), Enthalpy(H), Entropy(S), Free energy(G), Number of moles(n).

Reversible cyclic process.

According to Carnot’s Theorem, no engine working between two temperatures can be more efficient than a Carnot’s reversible engine working between the same temperatures.  

In a reversible process, the system and its surroundings return to the original states if the forward cycle is followed by the reverse cycle. Carnot engine is a theoretical thermodynamical cycle proposed by Leonard Carnot. It gives the estimate of the maximum possible efficiency that a heat engine during the conversion process of heat into work and conversely, working between two reservoirs can possess. Thus we can say that reversibility is the basis of an ideal engine.

An isothermal process is a change of a system, in which the temperature remains constant, ∆T = O.This typically occurs when a system is in contact with an outside thermal reservoir and the change takes place slowly to allow the system to continually adjust to the reservoir’s temperature through heat exchange.

Isothermal process takes place in any type of system that regulates the temperature. In the thermodynamic analysis of chemical reactions, it is first analyzed what happens under isothermal conditions. In an isothermal process, the internal energy of an ideal gas is constant. This is due to the fact that there are no intermoleculaf forces in an ideal gas. In the isothermal compression’of a gas, there is work done on the system to decrease the volume and increase the pressure. Doing work on the gas, can increase the internal energy and increase the temperature. For constant temperature, energy must leave the system. For an ideal gas, the amount of energy entering the environment is equal to the amount of work done on the gas, as the internal energy does not vary.

Adiabatic process is that process in which changed, but there is no transfer of heat between a thermodynamical system and its surroundings. In this process, energy is transferred only as work. This process provides a rigorous conceptual basis to explain the first law of Thermodynamics.

A process in which transfer of heat is not involved in the system, so that Q = 0, is called an adiabatic process. For example, the compression of a gas within an engine’s cylinder is assumed to take place so fast that on the time scale of the process of compression, little energy of the system can be transferred out as heat.

Essential conditions for an adiabatic process :

• The process of expansion or compression should be sudden, so that heat does not get time to get exchanged with the surroundings.
• The walls of the container must be perfectly insulated so that there cannot be any exchange of heat between the gas and surroundings.

Adiabatic process is that process in which temperature (T), pressure (P) and volume (V) can be changed, but there is no transfer of heat between a thermodynamical system and its surroundings. In this process, energy is transferred only as work. This process provides a rigorous conceptual basis to explain the first law of Thermodynamics.

A process in which transfer of heat is not involved in the system, so that Q = 0, is called an adiabatic process. For example, the compression of a gas within an engine’s cylinder is assumed to take place so fast that on the time scale of the process of compression, little energy of the system can be transferred out as heat.

Essential conditions for an adiabatic process:

• The process of expansion or compression should be sudden, so that heat does not get time to get exchanged with the surroundings.
• The walls of the container must be perfectly insulated so that there cannot be any exchange of heat between the gas and surroundings.

Answer: (a) state

η = 1 - T₁/T₁ = 1 - 273/373 = 0.27.

% Efficiency = [T₂ - T₁] x 100

T₁ = 110°C + 273 = 383 K.

T₂ = 25°C – 273 = 298 K.

% Efficiency = [(383 - 298) / 383] x 100

% Efficiency = [(85 x 100) / 383] 

% Efficiency = [8500 / 383] 

% Efficiency = 22.2%

Answer: (c) < 100%

Internal energy of a system is defined as the sum of the kinetic energies of the atoms and molecules belonging to the system, and the potential energies associated with the interactions between these constituents (atoms and molecules).

[Note : Internal energy does not include the potential energy and kinetic energy of the system as a whole. In the case of an ideal gas, internal energy is purely kinetic. In the case of real gases, liquids and solids, internal energy is the sum of potential and kinetic energies. For an ideal gas, internal energy depends on temperature only. In other cases, internal energy depends on temperature, as well as on pressure and volume. According to quantum theory, internal energy never becomes zero. Even at OK. particles have energy called zeropoint energy.]

(C) \(\frac32\) RT 

Argon is a monatamic gas. In this case, with three degrees of freedom, the average kinetic energy per molecule = \((\frac{3}2)\)k_BT, where k_B is the Boltzmann constant and T is the absolute (thermodynamic) temperature of the gas.

Hence, the internal energy of one mole of argon = N_A \((\frac{3}2)\)k_BT = \(\frac{3}2\)RT, where N_A is the Avogadro number and R = N_Ak_B is the universal gas constant. Oxygen is a diatomic gas. In this case, with five degrees of freedom at moderate temperatures, the internal energy of one mole of oxygen =\(\frac{3}2\)RT.

(C) \(\frac32\) RT 

The internal energy of one mole of argon at 300 K

= \(\frac32\)RT = \(\frac32\)(8.314)(300) J = 3741 J.

Correct option is (A) 8300J

u₁ = \(\frac52\)RT₁ and u₂ = \(\frac52\)RT₂

\(\therefore\) u_{2 =} u₁ \((\frac{T_2}{T_1})\) = (6235) \((\frac{400}{300})\) = 8313 J

This is the required quantity.

A process in which the thermodynamic state of a system is changed is called a thermodynamic process.

Example : Suppose a container is partially filled with water and then closed with a lid. If the container is heated, the temperature of the water starts rising and after some time the water starts boiling. The steam produced exerts pressure on the walls of the container,

Here, there is a change in the pressure, volume and temperature of the water, i.e. there is a change in the thermodynamic state of the system.

The mathematical relation between the state variables (pressure, volume, temperature, amount of the substance) is called the equation of state.

In the usual notation, the equation of state for an ideal gas is PV = nRT.

For a fixed mass of gas, the number of moles, n, is constant. R is the universal gas constant. Thus, out of pressure (P), volume (V) and thermodynamic temperature (T), only two (any two) are independent.

Similarities :

1. Heat is added to the system. 

2. There is increase in the internal energy of the system. 

3. Work is done by the system on its environment.

Differences : In a solar cooker, heat is supplied in the form of solar radiation. The rate of supply of heat is relatively low.

In a pressure cooker, usually LPG is used (burned) to provide heat. The rate of supply of heat v is relatively high.

As a result, it takes very long time for cooking when a solar cooker is used. With a pressure cooker, it does not take very long time for cooking.

[Note : A solar cooker can be used only when enough solar radiation is available.]

1. When an inflated balloon is punctured, the air inside it suddenly expands and escapes into the atmosphere. During the rapid expansion, there is no uniformity of pressure, temperature and density. 

2. When water is heated, there is no uniformity of pressure, temperature and density. If the vessel is open, some water molecules escape to the atmosphere.

A system is said to be in thermal equilibrium when its temperature is uniform throughout the system and does not change with time.