PhysicsKund Physics class 9 to 12 NCERT, JEE - NEET

Thermodynamic State Variables and Equation of State Every equilibrium state of a thermodynamic system is completely described by a set of macroscopic quantities known as Thermodynamic State Variables or State Functions . What are Thermodynamic State Variables? State variables are measurable physical quantities that define the state of a thermodynamic system when it is in thermodynamic equilibrium. For a gas, the common state variables are: Pressure ($P$) Volume ($V$) Temperature ($T$) Mass ($M$) Number of moles ($\mu$) These variables completely describe the equilibrium state of the system. Condition for State Variables State variables can only be assigned meaningful values when the system is in a state of thermodynamic equilibrium. In equilibrium: Temperature is uniform throughout the system. Pressure is uniform throughout the system. No net macroscopic changes occur with time. Non-Equilibrium States When a system changes rapidly, pressure and temper...

Notes : Thermal Equilibrium: Adiabatic & Diathermic Walls | Class 11 Physics 1. Defining Thermal Equilibrium The concept of equilibrium has different meanings in mechanics and thermodynamics. Mechanical Equilibrium A system is said to be in mechanical equilibrium when the net external force and the net torque acting on it are zero. This condition is related to motion, forces, and balance. Thermodynamic Equilibrium A system is said to be in thermodynamic equilibrium if the macroscopic variables that characterize the system do not change with time. Macroscopic Variables Include: Pressure (P) Volume (V) Temperature (T) Mass Composition Example Consider a gas enclosed in a closed, rigid container that is completely insulated from its surroundings. If its pressure, volume, temperature, mass, and composition remain constant with time, the gas is said to be in a state of thermodynamic equilibrium. 2. Influence of Boundary Walls Whethe...

Internal Energy, Heat and Work 1. Internal Energy (U) Internal energy is the total microscopic energy possessed by a thermodynamic system. Definition It is the sum of: Kinetic Energy of molecules due to: Translational motion Rotational motion Vibrational motion Potential Energy due to intermolecular forces between molecules. Therefore, U =  Total Molecular Kinetic Energy + Total Molecular Potential Energy Important Points Internal energy includes only the random microscopic motion of molecules. It does not include the kinetic energy of the entire system moving as a whole. It is measured in a frame where the centre of mass of the system is at rest . Example: A gas inside a cylinder possesses internal energy due to molecular motion. If the cylinder is thrown upward, the kinetic energy of the moving cylinder is not part of its internal energy. State Variable Internal energy is a state function (state variable...

Zeroth Law of Thermodynamics The Zeroth Law of Thermodynamics is the most fundamental law of thermodynamics. It introduces the concept of temperature and provides the basis for measuring temperature. The law explains thermal equilibrium and forms the foundation of all temperature-measuring devices. Introduction In everyday life, we compare objects by saying that one object is hotter or colder than another. To make this comparison scientifically, we need a measurable quantity called temperature . The Zeroth Law of Thermodynamics provides the scientific basis for defining temperature. Statement of Zeroth Law If two thermodynamic systems are separately in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. In simple words, if System A has the same temperature as System C, and System B also has the same temperature as System C, then Systems A and B must have the same temperature. Thermal Equilibrium Thermal equilibrium is the ...

Second Law of Thermodynamics – Definition, Statements, Limitations, FAQ & Quiz The Second Law of Thermodynamics is one of the most important laws of physics. While the First Law explains the conservation of energy, the Second Law explains the direction of natural processes and the limitations on the conversion of heat into work. Need for the Second Law of Thermodynamics The First Law of Thermodynamics states that energy can neither be created nor destroyed. However, it does not tell us whether a process can occur naturally or not. For example, a book lying on a table could theoretically absorb heat from the table and convert that heat completely into mechanical energy to jump upward. Such a process would satisfy the First Law because energy is conserved. But such a process never occurs in nature. Therefore, another law is needed to determine which processes are possible and which are impossible. This requirement leads to the Second Law of Thermodynamics. Limitat...

Thermodynamics – Introduction 1. Introduction In the previous chapter, we studied the thermal properties of matter. In this chapter, we study the laws governing thermal energy and the conversion of heat into work and vice versa. Examples of Heat and Work Conversion Rubbing of Palms: In winter, when we rub our palms together, the work done against friction produces heat and our hands become warm. Steam Engine: In a steam engine, the heat energy of steam is used to do useful work in moving the piston, which rotates the wheels of the train. Energy Conversion: \[ \text{Work} \rightarrow \text{Heat} \] \[ \text{Heat} \rightarrow \text{Work} \] 2. Historical Concept of Heat In physics, concepts like heat, temperature and work must be defined carefully. Historically, it took a long time to understand the true nature of heat. Caloric Theory of Heat According to the old caloric theory, heat was regarded as a fine invisible fluid called caloric present insid...

Notes : Chapter 11 Thermodynamics Class 11 Physics - Physicskund  11.1 Introduction 11.2 Thermal equilibrium 11.3 Zeroth law of Thermodynamics 11.4 Heat, internal energy and work 11.5 First law of thermodynamics 11.6 Specific heat capacity 11.7 Mayer Formula proof 11.8 Thermodynamic state variables and equation of state 11.9 Thermodynamic processes 11.10 Second law of thermodynamics 11.11 Reversible and irreversible processes 11.12  Carnot engine

Carnot Engine: Definition, Working, Carnot Cycle and Efficiency | Class 11 Physics Notes The Carnot engine is one of the most important concepts in thermodynamics. It is an ideal heat engine that operates on a completely reversible cycle called the Carnot cycle . The Carnot engine establishes the maximum possible efficiency that any heat engine can achieve while operating between two thermal reservoirs. Since no real engine can be completely reversible, the Carnot engine serves as the benchmark against which the performance of all practical heat engines is compared. In this article, we will study the definition, history, construction, working, Carnot cycle, detailed derivation of efficiency, Carnot theorem, universal relation, applications, limitations, important formulas, FAQs, and MCQs. History of Carnot Engine In 1824, the French engineer Sadi Carnot investigated an important question: What is the maximum possible efficiency of a heat engine operating between two ther...

Comparison of the Slopes and Work done of an Isothermal and an Adiabatic Curve Comparison of the Slopes of an Isothermal and an Adiabatic Curve Isothermal Process :  For an isothermal process, $PV = \text{constant}$ Differentiating, $PdV + VdP = 0$ $\left(\frac{dP}{dV}\right)_{\text{iso}} = -\frac{P}{V}$ This represents the slope of the isothermal curve. Adiabatic Process For an adiabatic process, $PV^\gamma = \text{constant}$ Differentiating, $P\,\gamma V^{\gamma - 1} dV + V^\gamma dP = 0$ $\left(\frac{dP}{dV}\right)_{\text{adi}} = -\gamma \frac{P}{V}$ Comparison :  From equations above, $\left(\frac{dP}{dV}\right)_{\text{adi}} = \gamma \left(\frac{dP}{dV}\right)_{\text{iso}}$ Since $(\gamma > 1 )$, therefore, $\left(\frac{dP}{dV}\right)_{\text{adi}} > \left(\frac{dP}{dV}\right)_{\text{iso}}$ Conclusion:  The slope of the adiabatic curve is steeper than that of the isothermal curve. Comparison of Work Done During Isothermal and Adiabatic Processes  Show that w...

Work Done During Isochoric Process We know, work done ( dW = P dV). In an isochoric process, volume (V) is constant, so (dV = 0). Hence, work done during an isochoric process is zero. According to the First Law of Thermodynamics: $\Delta Q = \Delta U + \Delta W$ Since ( $\Delta W = 0$), so ( $\Delta Q = \Delta U$). Thus, the heat absorbed by the system (or gas) is used to change the internal energy and hence the temperature of the system (or gas). Work Done During Isobaric Process Work done: $dW = P dV = P(V_{2} - V_{1})$ In an isobaric process, (P) is constant. Now, $P V_{1} = \mu R T_{1}$ and $P V_{2} = \mu R T_{2}$ $dW = P(V_{2} - V_{1}) = \mu R (T_{2} - T_{1})$ According to the First Law of Thermodynamics: $\Delta Q = \Delta U + \Delta W$ Therefore, heat absorbed b the system is partly used to change its internal energy and partly used to do work.

Consider n mole of an ideal gas contained in an insulating cylinder fitted with a perfectly insulating piston of area of cross section area A. Let the volume of the gas be V and it exerts a pressure P on the walls of the cylinder and the piston . Due to this pressure ( if greater than the external pressure ) , the gas expands and piston moves through a small distance dx.  Force acting on the piston , F = PA External work done by the gas is given by  dW = Fdx = PA dx = PdV If the gas expands from initial volume ($V_{1}$) to the final volume ($V_{2}$), the total work  Step 1: Use the Adiabatic Condition For a reversible adiabatic process: $PV^\gamma = \text{constant} = K$ Also, from the ideal gas law: $PV = nRT$ Step 2: Express Work as an Integral The work done by the gas is: $W = \int_{V_1}^{V_2} P \, dV$ Using the adiabatic condition ( $P = \frac{K}{V^\gamma}$), we get: $W = \int_{V_1}^{V_2} \frac{K}{V^\gamma} \, dV = K \int_{V_1}^{V_2} V^{-\gamma} \, dV$ $W = K \left[ \f...

Expression For Work Done During isothermal Process - Thermodynamics  Consider one mole of an ideal gas contained in a perfectly conducting cylinder fitted with a perfectly frictionless piston of area of cross section area A. Let the volume of the gas be V exerting a pressure P on the walls of the cylinder and the piston. Let the gas expands and the piston moves through a small distance dx. Force acting on the piston , F = PA $\therefore$ work done to move the piston through a distance dx is given by $dW = Fdx= PA dx = PdV$ To find the total work done from volume $( V_1) to ( V_2)$: $W = \int_{V_1}^{V_2} P \, dV$ Step 2: Use the Ideal Gas Law For an ideal gas: $PV = nRT \Rightarrow P = \frac{nRT}{V}$ Substituting into the work integral: $W = \int_{V_1}^{V_2} \frac{nRT}{V} \, dV$ Step 3: Take Constants Outside the Integral Since \( n \), \( R \), and \( T \) are constants during an isothermal process: $W = nRT \int_{V_1}^{V_2} \frac{1}{V} \, dV$ Step 4: Integrate $\int_{V_1}^{V_2} \f...

Proof of Mayer's Relation We know that: Ideal Gas Equation: $$PV=nRT$$ First Law of Thermodynamics: $$\Delta Q=\Delta U+W$$ Step 1: Constant Volume Process At constant volume, $$\Delta V=0$$ Therefore, the work done is $$W=P\Delta V=0$$ Substituting into the first law of thermodynamics: $$\Delta Q=\Delta U$$ For an ideal gas, $$\Delta U=nC_v\Delta T$$ Hence, $$\Delta Q=nC_v\Delta T$$ Step 2: Constant Pressure Process At constant pressure, the work done is $$W=P\Delta V$$ Using the first law of thermodynamics, $$\Delta Q=\Delta U+P\Delta V$$ For a temperature change $$\Delta T$$, $$\Delta Q=nC_p\Delta T$$ and $$\Delta U=nC_v\Delta T$$ Substituting these values: $$nC_p\Delta T=nC_v\Delta T+P\Delta V$$ Step 3: Using the Ideal Gas Equation From the ideal gas equation, $$PV=nRT$$ Differentiating for constant pressure: $$P\Delta V=nR\Delta T$$ Step 4: Substitution and Simplification Substituting $$P\Delta V=nR\Delta T$$ ...

Specific Heat Capacity: Definition, Formula, Units, Dimensions Introduction When a quantity of heat ($\Delta Q$) is supplied to a substance, its temperature changes from an initial temperature $T$ to a final temperature $T+\Delta T$. Heat Capacity Definition Heat capacity is the amount of heat required to raise the temperature of a body by one kelvin. Formula $$S=\frac{\Delta Q}{\Delta T}$$ SI Unit J K -1 Dimensions $$[S]=[ML^2T^{-2}K^{-1}]$$ Specific Heat Capacity Definition Specific heat capacity is the amount of heat required to raise the temperature of unit mass of a substance by one kelvin. Formula $$s=\frac{\Delta Q}{m\Delta T}$$ $$s=\frac{S}{m}$$ $$\Delta Q=ms\Delta T$$ SI Unit J kg -1 K -1 Dimensions $$[s]=[L^2T^{-2}K^{-1}]$$ Molar Specific Heat Capacity Definition When the amount of substance is expressed in moles, the heat capacity per mole is called molar specific heat capacity. Formula $$C=\frac{\Delta Q}{n\Delta T}$$ ...

First Law of Thermodynamics The First Law of Thermodynamics is the law of conservation of energy applied to thermodynamic systems. It states that the heat supplied to a system is equal to the increase in its internal energy plus the work done by the system. Mathematical Equation $$\Delta Q = \Delta U + \Delta W$$ Where: ΔQ = Heat supplied to the system ΔU = Change in internal energy ΔW = Work done by the system For expansion against constant pressure: $$\Delta W = P\Delta V$$ Physical Significance of First Law of Thermodynamics The First Law explains the relationship between heat, work and internal energy. Heat supplied may increase internal energy. Heat supplied may be converted into work. Total energy remains conserved. First Law in Different Thermodynamic Processes 1. Isothermal Process Temperature remains constant. $$\Delta T = 0$$ For an ideal gas: $$\Delta U = 0$$ Therefore: $$\Delta Q = \Delta W$$ 2. Isochoric Process Volume remain...