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Physics – Thermodynamics

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    Study Guide Physics – Thermodynamics 1. Development of the Ideal Gas Law Gases may look simple, but their behavior follows clear scientific rules. Scientists discovered these rules by doing careful experiments over many years. Some of the key contributors were Robert Boyle , Jacques Charles , and Joseph Gay - Lussac . Together, their work led to what we now call the Ideal Gas Law . An ideal gas is a model used to understand real gases. In this model, gas particles are identical, very small, 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 on Earth. However, gases inside the Sun do not behave ideally because the temperatures and pressures there are extremely high. 1. Boyle’s Law: Pressure and Volume Boyle’s Law explains what happens to a gas when temperature stays constant . • When a gas is compressed , its pressure increases . • When a gas expands , its pressure decreases . This means pressure and volume are inversely related . Mathematical form: If a gas changes from one state to another: • (P) and (V) are the original pressure and volume • (P') and (V') are the new pressure and volume So, if pressure doubles, volume becomes half (as long as temperature does not change).

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    Study Guide 2. Charles’ and Gay - Lussac’s Law: Volume and Temperature This law describes how gases behave when pressure is kept constant . • As temperature increases , volume increases . • As temperature decreases , volume decreases . Here, temperature must be measured in Kelvin (K) . Mathematical form: This explains why a balloon expands in warm air and shrinks in cold air. 3. Combining Boyle’s Law and Charles’ Law When we combine both laws, we see that: This shows that gas volume depends on pressure , temperature , and also on the amount of gas present. For example: • Pumping more air into a tire increases the mass of gas . • More gas particles mean a larger volume at the same pressure and temperature. 4. Definition of a Mole To measure how much gas we have, scientists use the unit called a mole (mol) . • A mole tells us the number 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/mol Example: Lead has an atomic mass of 207 g/mol . So, 207 g of lead = 1 mole of lead . 5. The Ideal Gas Law When Boyle’s Law, Charles’ Law, and the concept of moles are combined, we get the Ideal 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 = 8.31 J/mol] 6. The Combined Gas Law If the number of moles stays the same , the Ideal Gas Law can be rearranged to compare two different sets of conditions: This is useful when pressure, volume, and temperature all change.

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    Study Guide 7. 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 liters 8. Avogadro’s Number Amedeo Avogadro proposed that equal volumes of gases at the same temperature and pressure contain the same number of molecules . Using this idea, the Ideal Gas Law can also be written as: where: • (N) = number of molecules • (k) = Boltzmann’s constant 9. Kinetic Theory of Gases The kinetic theory of gases explains gas behavior by looking at the motion of gas molecules. Main assumptions: • Gas molecules are in constant random motion • Collisions between molecules and container walls are elastic • Molecules are very far apart compared to their size • The average velocity of all molecules is zero

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    Study Guide 10. Pressure from Molecular Motion From 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 the average kinetic energy of molecules 11. Temperature and Kinetic Energy By 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 pressure This beautifully connects the microscopic world of molecules with the macroscopic properties we observe, like pressure and temperature. 2. Heat 1. Heat vs Temperature Heat and temperature are not the same thing . • Temperature tells us how hot or cold an object is. • Heat is a form of energy that flows from one object to another. When two objects at different temperatures touch, heat always flows from the hotter object to the colder one until both reach the same temperature.

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    Study Guide Heat is a type of energy, and any increase in heat energy in a system is matched by an equal decrease in another form of energy (such as mechanical energy), and vice versa. 2. Heat Capacity and Specific Heat The heat capacity of an object is the amount of heat required to raise its temperature by 1 degree . Imagine blocks made of different metals , all with: • The same mass • Heated to the same temperature When these blocks are placed on ice, they melt different amounts of ice . This happens because different materials store and release heat differently. This difference is due to specific heat . Specific Heat (c) Specific heat is the heat capacity per unit mass .

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    Study Guide Where: • (Q) = heat added (or removed) • (m) = mass of the substance • ( Δ T) = change in temperature Specific heat values are known for many materials and can be found in tables. 3. Mechanical Equivalent of Heat The calorie is a unit of heat energy. • 1 calorie = energy needed to raise 1 g of water by 1°C • 1 kilocalorie (kcal) = energy needed to raise 1 kg of water by 1°C o (Food “Calories” are actually kilocalories.) In SI units: 1 calorie = 4.184 joules Another unit is the British Thermal Unit (BTU) : BTU = 252 calories = 1.054 kJ These relationships show that heat energy and mechanical work are equivalent , which is called the mechanical equivalent of heat .

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    Study Guide 4. Heat Transfer Formula The amount of heat transferred into or out of an object is: Q = mc Δ T • (Q > 0): heat gained • (Q < 0): heat lost In heat exchange problems, we usually assume the system is thermally isolated , meaning no heat is lost to the surroundings. 5. Calorimetry Calorimetry is the study of heat transfer. A calorimeter is a device used to measure the specific heat of a substance . How it works: • A hot object of unknown specific heat is placed into water. • The water has a known 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 Situation A hot metal block of mass (m m ) and initial temperature (T m o is placed into cool water of mass (m w ) and temperature (T wo . After equilibrium, both reach temperature (T f ).

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    Study Guide 6. Phase Changes A phase change occurs when a substance changes state: • Solid ↔ Liquid • Liquid ↔ Gas Examples: • Melting • Freezing • Boiling • Condensation 7. Latent Heat During a phase change, temperature remains constant , even though heat is still being added or removed. The heat required for a phase change is called latent heat (L) : (L) : Q = mL

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