Physics – Thermodynamics - Quick Guides | Physics

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Study GuidePhysics–Thermodynamics1.Development of the Ideal Gas LawGases may look simple, but their behavior follows clear scientific rules. Scientists discovered theserules by doing careful experiments over many years. Some of the key contributors wereRobertBoyle,Jacques Charles, andJoseph Gay-Lussac.Together, their work led to what we now call theIdeal Gas Law.Anideal gasis a model used to understand real gases. In this model, gas particles are identical, verysmall, and interact only during brief, elastic collisions—like perfectly bouncing billiard balls.Most real gases behave very much like ideal gases under everyday temperatures and pressures onEarth. However, gases inside the Sun donotbehave ideally because the temperatures andpressures there are extremely high.1.Boyle’s Law: Pressure and VolumeBoyle’s Law explains what happens to a gas whentemperature stays constant.•When a gas iscompressed, itspressure increases.•When a gasexpands, itspressure decreases.This means pressure and volume areinversely related.Mathematical form:If agas changes from one state to another:•(P) and (V) are the original pressure and volume•(P') and (V') are the new pressure and volumeSo, if pressure doubles, volume becomes half (as long as temperature does not change).

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Study Guide2.Charles’ and Gay-Lussac’s Law: Volume and TemperatureThis law describes how gases behave whenpressure is kept constant.•Astemperature increases,volume increases.•Astemperature decreases,volume decreases.Here, temperature must be measured inKelvin (K).Mathematical form:This explains why a balloon expands in warm air and shrinks in cold air.3.Combining Boyle’s Law and Charles’ LawWhen we combine both laws, we see that:This shows that gas volume depends onpressure,temperature, and also on theamount of gaspresent.For example:•Pumping more air into a tire increases themass of gas.•More gas particles mean a larger volume at the same pressure and temperature.4.Definition of a MoleTo measure how much gas we have, scientists use the unit called amole (mol).•A mole tells us thenumber of particles, not just the mass.•The number of moles (n) is given by:

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Study Guide•[n = m/M]where:(m) = mass of the gas(M) = molar (atomic or molecular) mass in g/molExample:Lead has an atomic mass of207 g/mol.So,207 g of lead = 1 mole of lead.5.The Ideal Gas LawWhen Boyle’s Law, Charles’ Law, and the concept of moles are combined, we get theIdeal Gas Law:[PV = nRT]Here:•(P) = pressure (in pascals, Pa)•(V) = volume (in cubic meters, m³)•(n) = number of moles•(T) = temperature (in Kelvin)•(R) = universal gas constant•[R = 8.31J/mol]6.The Combined Gas LawIf thenumber of moles stays the same, the Ideal Gas Law can berearranged to compare twodifferent sets of conditions:This is useful when pressure, volume, and temperature all change.

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Study Guide7.Standard Temperature and Pressure (STP)Scientists often compare gases under standard conditions:•Standard pressure:1 atmosphere (atm)•Standard temperature:0°C (≈ 273 K)At STP:•1 mole of any ideal gas occupies 22.4 liters8.Avogadro’s NumberAmedeo Avogadroproposed that equal volumes of gases at the same temperature and pressurecontain thesame number of molecules.Using this idea, the Ideal Gas Law can also be written as:where:•(N) = number of molecules•(k) = Boltzmann’s constant9.Kinetic Theory of GasesThekinetic theory of gasesexplains gas behavior by looking at the motion of gas molecules.Mainassumptions:•Gas molecules are inconstant random motion•Collisions between molecules and container walls areelastic•Molecules are very far apart compared to their size•The average velocity of all molecules is zero

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Study Guide10.Pressure from Molecular MotionFrom Newton’s laws, pressure can be related to molecular motion:This shows:•Pressure depends on how many molecules are in a given volume•Pressure also depends on theaverage kinetic energyof molecules11.Temperature and Kinetic EnergyBy combining this equation with the Ideal Gas Law:This means:•Temperature is a direct measure of average molecular kinetic energy•Higher temperature → faster-moving molecules → higher pressureThis beautifully connects themicroscopic world of moleculeswith themacroscopic propertiesweobserve, like pressure and temperature.2.Heat1.Heat vs TemperatureHeat and temperature arenot the same thing.•Temperaturetells us how hot or cold an object is.•Heatis a form ofenergythat flows from one object to another.When two objects at different temperatures touch,heat always flows from the hotter object to thecolder oneuntil both reach the same temperature.

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Study GuideHeat is a type of energy, and any increase in heat energy in a system is matched by an equaldecrease in another form of energy (such as mechanical energy), and vice versa.2.Heat Capacity and Specific HeatTheheat capacityof an object is the amount of heat required to raise its temperature by1 degree.Imagine blocks made ofdifferent metals, all with:•Thesame mass•Heated to thesame temperatureWhen these blocks are placed on ice, they meltdifferent amounts of ice.This happens because different materials store and release heat differently.This difference is due tospecific heat.Specific Heat (c)Specific heat is theheat capacity per unit mass.

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Study GuideWhere:•(Q) = heat added (or removed)•(m) = mass of the substance•(ΔT) = change in temperatureSpecific heat values are known for many materials and can be found in tables.3.Mechanical Equivalent of HeatThecalorieis a unit of heat energy.•1 calorie= energy needed to raise1 g of water by 1°C•1 kilocalorie (kcal)= energy needed to raise1 kg of water by 1°Co(Food “Calories” are actuallykilocalories.)In SI units:1 calorie=4.184 joulesAnother unit is theBritish Thermal Unit (BTU):BTU = 252 calories = 1.054 kJThese relationships show thatheat energy and mechanical work are equivalent, which is calledthemechanicalequivalent of heat.

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Study Guide4.Heat Transfer FormulaThe amount of heat transferred into or out of an object is:Q=mcΔT•(Q > 0): heat gained•(Q < 0): heat lostIn heat exchange problems, we usually assume the system isthermally isolated, meaning no heat islost to the surroundings.5.CalorimetryCalorimetryis the study of heat transfer.Acalorimeteris a device used to measure thespecific heat of a substance.How it works:•A hot object ofunknown specific heatis placed into water.•The water has aknown mass and specific heat.•Heat lost by the object = heat gained by the water.•Once thermal equilibrium is reached, the specific heat of the object can be calculated.Example SituationA hot metal block of mass (mm) and initialtemperature (Tmois placed into cool water of mass (mw) andtemperature (Two.After equilibrium, both reach temperature (Tf).

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Study Guide6.Phase ChangesAphase changeoccurs when a substance changes state:•Solid↔Liquid•Liquid↔GasExamples:•Melting•Freezing•Boiling•Condensation7.Latent HeatDuring a phase change,temperature remains constant, even though heat is still being added orremoved.The heat required for a phase change is calledlatent heat (L):(L):Q=mL

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