11th Physics Book - Heat and Thermodynamics PDF

# 11th Physics Book UNIT 8: HEAT AND THERMODYNAMICS ## 8.1 Thermal Equilibrium * Two systems are in thermal equilibrium with each other if they are at the same temperature. * Temperature is the main property that determines whether two systems will be in thermal equilibrium or not. * When two bodi...

# 11th Physics Book UNIT 8: HEAT AND THERMODYNAMICS ## 8.1 Thermal Equilibrium * Two systems are in thermal equilibrium with each other if they are at the same temperature. * Temperature is the main property that determines whether two systems will be in thermal equilibrium or not. * When two bodies at different temperatures are connected by a diathermic substance, the heat starts flowing between them, from the high-temperature body to the lower temperature body, until their temperature becomes equal. ### 8.1.1 Internal Energy * Internal energy is the sum of all the molecular energies of a substance. * Internal energy can increase by heating and doing mechanical work. * Internal energy is a state function, meaning it depends on the initial and final states of the system, not on the path followed. * The internal energy of an ideal gas is directly proportional to its temperature. ### 8.1.2 Ideal Gas Equation * The ideal gas equation is: $PV = nRT$ * P is pressure * V is volume * n is the number of moles * R is the ideal gas constant ($8.314 Jmol^{-1}K^{-1}$) * T is the absolute temperature * Boltzmann's constant, k, is derived from the ideal gas constant: $k = \frac{R}{N_A} = 1.38 \times 10^{-23} JK^{-1}$ * The average translational kinetic energy of molecules in a gas is: <Κ.Ε.> $= \frac{3}{2}kT$ ### 8.1.3 Applications of Ideal Gas Equation * This equation can explain how gas molecules affect the characteristics of gases like temperature and pressure. * This equation relates the macroscopic properties of gases to their microscopic properties. ## 8.2 Kinetic Theory of Gases * According to the kinetic theory of gases, gas is made up of a number of tiny hard spheres (molecules) that collide with each other and the container walls. This explains how the motion of the molecules affects the properties of the gas. * Gases at low pressure and high temperatures behave more like ideal gases. ### 8.2.1 Work in Thermodynamics * Work represents the transfer of energy by some means. * Work = Force x Displacement * Pressure-volume work can be calculated by considering the change in volume of a gas under a constant pressure: $W = P\Delta V$ ## 8.3 The Gas Laws * **Boyle's Law**: The volume of a given amount of gas at a constant temperature is inversely proportional to the pressure applied: $V \propto \frac{1}{P}$ or $PV = constant$. * **Charles's Law**: The volume of a given amount of gas at a constant pressure is directly proportional to the absolute temperature: $V \propto T$ or $V/T = constant$. * **Gay Lussac's Law**: The pressure of a given amount of gas at a constant volume is directly proportional to the absolute temperature: $P \propto T$ or $P/T = constant$. ## 8.4 First Law of Thermodynamics * The first law of Thermodynamics states that the total energy of an isolated system remains constant. * Energy can be transferred from one form to another, but it cannot be created or destroyed. * Mathematically, the first law of thermodynamics can be written as: $Q = \Delta U + W$ where: * $Q$ is the heat added to the system * $\Delta U$ is the change in internal energy of the system * $W$ is the work done by the system. ### 8.4.1 Isothermal Process * Isothermal process is a thermodynamic process in which temperature remains constant throughout the process. * In this process, work and energy are expended to maintain an equal temperature at all times. * In an isothermal process, the product of pressure and volume remains constant: $PV = constant$. ### 8.4.2 Adiabatic Process * An adiabatic process is a thermodynamic process in which no heat or mass transfer occurs between a system and its surroundings. * In this process, energy is transferred only as work. * The first law of thermodynamics for an adiabatic process can be written as: $\Delta U = -W$, where: * $ \Delta U $ is the internal energy * $W$ is the work done by the system. ### 8.4.3 Isochoric Process * An isochoric process is a thermodynamic process in which the volume of the system remains constant. * In this process, all the heat given to the system is used to increase its internal energy: $Q = \Delta U$, where: * $Q$ is the heat added to the system * $ \Delta U $ is the internal energy ### 8.4.4 Isobaric Process * An isobaric process is a thermodynamic process in which the pressure of the system remains constant. * In this process, heat is transferred to the system, some work is done, and there is a change in the internal energy of the system. ## 8.5 Heat Engine * A heat engine is a device that converts heat energy into mechanical work. * It consists of three main parts: * A hot reservoir (source of heat) * A cold reservoir (heat sink) * A working substance (usually a gas) ## 8.6 Reversible and Irreversible Process * A reversible process is a process that can be retraced in exactly reverse order, without bringing any change in its surroundings. * An irreversible process is a process that cannot be retraced in exactly reverse order without bringing a change to its surroundings. * A cyclic process is a succession of events that bring the system back to its initial condition. ## 8.7 Second Law of Thermodynamics * The second law of thermodynamics deals with the direction of heat flow and the conditions under which heat can be converted into work. * **Kelvin Planck Statement**: It is impossible for a heat engine to convert heat taken from a single reservoir entirely into work without leaving any change in the working system. * **Clausius Statement**: It is impossible to cause heat to flow from a cold body to a hot body without the expenditure of work. ## 8.8 Carnot's Engine * A Carnot heat engine is a theoretical engine that operates on the Carnot cycle. * The Carnot cycle is a reversible cycle that consists of four steps: * Isothermal Expansion: This step is performed at a constant temperature. The gas absorbs heat from the hot reservoir expanding isothermally. * Adiabatic Expansion: This step occurs in an insulated cylinder, where the gas expands without the exchange of heat. * Isothermal Compression: This step is performed at a constant temperature. The gas is compressed isothermally, rejecting heat to the cold reservoir. * Adiabatic Compression: This step occurs in an insulated cylinder, where the gas is compressed without the exchange of heat. ### 8.8.1 Efficiency of Carnot Engine * The efficiency of a Carnot engine is given by: $\eta = \frac{W}{Q_h} = 1 - \frac{T_c}{T_h}$ where: * $\eta$ is the efficiency of the Carnot engine * $W$ is the work done by the engine * $Q_h$ is the heat absorbed by the engine * $T_c$ is the temperature of the cold reservoir * $T_h$ is the temperature of the hot reservoir ## 8.9 Refrigerator * A refrigerator is a device that removes heat from a region at a lower temperature than its surroundings. * It works by using a working substance (usually a gas) to absorb heat from the cold reservoir and reject it to the hot reservoir. * The coefficient of performance (CP) of a refrigerator is defined as the ratio of the amount of heat removed from the cold reservoir to the work required to do so: $CP = \frac{Q_c}{W}$ ## 8.10 Entropy * Entropy is a thermodynamic quantity that represents the unavailability of a system's thermal energy for conversion into mechanical work. * Entropy is a measure of disorder or randomness in a system. * The change in entropy of a system is given by: $\Delta S = \frac{\Delta Q}{T}$ * $\Delta S$ is the change in entropy * $\Delta Q$ is the amount of heat added to the system * $T$ is the absolute temperature ### 8.10.1 Sign Convention for Entropy * The change in entropy is positive if heat is added to the system. * The change in entropy is negative if heat is removed from the system. ### 8.10.2 Entropy and Energy * Entropy requires a particular direction for time known as "Arrow of time". As one goes "forward" in time, the entropy of an isolated system increases. This is why entropy measurements are a way of distinguishing the past from the future. * For all reversible processes, the entropy of the system remains constant. * For all irreversible processes, the entropy of the system increases.