Exam 3 Definitions and Derivations PDF

Exam 3 Definitions and Derivations Study online at https://quizlet.com/_fy06wm Write the ratio of two Kelvin temperatures as the ratio of the (T_2/T_1) = (p_2/p_1) corresponding pressures in a const...

Exam 3 Definitions and Derivations Study online at https://quizlet.com/_fy06wm Write the ratio of two Kelvin temperatures as the ratio of the (T_2/T_1) = (p_2/p_1) corresponding pressures in a constant-volume gas thermometer. L=± L_0 T Write the formulae for thermal expansion. V = ²V_0 T (for solids, ² = 3±) Q = mcT (c = specific heat) Write the equation the the quantity of heat required to change Q = nCT (C = molar heat capacity) temperature of a certain mass. dQ = mcdT State the equation for heat transfer in a phase change. Q = ±mL (L = heat of fusion/vaporization/etc.) A measure of the average kinetic energy of the particles in a Define temperature. substance (degrees K/F/C). If a system C is initially in thermal equilibrium with both systems Recall the Zeroth Law of Thermodynamics. A and B, then A and B are also in thermal equilibrium with each other. (all same temps) Two systems are in thermal equilibrium if and only if they have the Define the condition for thermal equilibrium. same temperature. As temperature increases, pressure increases at a proportional Explain how a constant-volume gas thermometer works. rate, so one can be measured to determine the other. Identify on a pressure-temperature plot how we know of an ab- As pressure approaches 0, T approaches -273.15 K = absolute solute zero on the Kelvin temperature scale. zero. Freezing water: C = 0, F = 32, K = 273.15 Explain the relationships between three main temperature scales Boiling water: C = 100, F = 212, K = 373.15 (Fahrenheit, Celsius, and Kelvin) by recalling the boiling and Therefore, Celsius and Kelvin both increase/decrease at the same freezing temperatures of water. rate, while Fahrenheit is just weird. Temperature changes correlate with changes in energy. Higher Explain on a molecular level why objects expand and contract with temperature readings mean that there is more motion occurring changes in temperature. on the molecular level. Molecules with motion therefore have the energetic capacity to occupy more space than cold molecules. Proved that heat and mechanical energy/work are completely Describe the significance of Sir James Joule's experiment linking convertible (foundation of the law of conservation of energy). Led heat and energy. the way for thermodynamics as a field of physics to exist. Now have a new way to view essentially any system involving heat. The amount of heat energy required to raise the temperature of a Define specific heat. mass amount of a given substance by a given temperature range (usually one degree). Once a problem has been identified as a calorimetry problem, de- termine what changes occur in the problem (temp/phase change), Demonstrate the process by which to solve calorimetry problems. assign variables, and set the sum of all heat energies equal to zero (energy conserved). pV = nRT = nk_B T State the ideal gas law equations and the gas constant. R = k_B N_A = 8.314 J/mol*K Write the formula for the average translational kinetic energy per (1/2)m(v^2)avg = (3/2)k_B T gas molecule. Write the formulae for the root-mean-square speed of a gas v_rms = sqrt((v^2)avg) molecule. Write the molar heat capacities at constant volume for a gas and C_V = (f/2)R ideal monatomic solid C_V = 3R State the Maxwell-Boltzmann velocity distribution. f(v) v^2 e^(m(v^2)/2kT) State Avagadro's number. Approximately 6.022 x 10^23 mol^-1. State the Boltzmann constant. k_B = R/N_A = 1.381 × 10^23 J/molecule · K m_total = nM Write the relationships between mass, molar mass, moles and m_molecule = M/N_A molecules. n = N/N_A 1/4  Exam 3 Definitions and Derivations Study online at https://quizlet.com/_fy06wm NOT EXPLICITLY TESTED: Write the mean free path equation for » =vt_mean = V(4À(2) r^2 N)^-1 a gas molecule. Pressure on the y-axis and Volume on the x-axis. Visually demon- strates the relationship between the two variables as a gas un- Describe and properly interpret pV-diagrams. dergoes some change. Area under the curve = work done by the gas. Certain characteristics define different processes (adiabatic, isothermal, etc.). Total Mass - total amount of mass within a substance = nM Molar Mass - mass of one mole of a certain substance Know the differences and relationships between total mass, molar # Of Moles - How many moles are there = m/M mass, number of moles, and number of molecules. # Of Molecules - How many molecules are there (6.022 x 10^23 molecules per mole) 1 - A container of volume V contains a very large number N of molecules, each with a molecular mass m. 2 - These molecules are point particles State the assumptions utilized for the kinetic-molecular model. 3 - The molecules are constantly moving and have elastic colli- sions with both themselves and the container walls. 4 - The container walls are perfectly rigid and are effectively infinitely as large as a molecule. 1. Based off of the assumptions required for the Kinetic-Molecular Model, v^2 = v_x^2 + v_y^2 + v_z^2. 2. Apply (1) for the average velocities of all molecules present: (v^2)_avg = (v_x^2)_avg + (v_y^2)_avg + (v_z^2)_avg. 3. In this model, v_x = v_y = v_z, so therefore (v_x^2)_avg = Derive the equation for the average translational kinetic energy of (1/3)(v^2)_avg an ideal gas. 4. Through rearranging the definition of pressure with re- spect to the current model, pV = (1/3)Nm(v^2)_avg --> (2/3)Nm((1/2)m(v^2)_avg) 5. Recognizing that the definition of kinetic energy has appeared: pV = (2/3)K_translational 6. Rearrange and apply the ideal gas law: K_tr = (3/2)nRT. Mean Free Time = the average time (t_mean) between particle collisions = V/4À(2) r^2 vN. Describe the mean free time and path of a gas particle. Mean Free Path = the average distance a particle travels between collisions. Explain the Maxwell-Boltzmann distribution of speeds of ideal gas Describes the true spread of molecular speeds throughout a gas: molecules. f(v) = 4À( m/2À kT) ^(3/2) v^2 e^(-mv^2/2kT) A pVT-surface represents the relationship between pressure (p), volume (V), and temperature (T) of a substance in 3D, showing how these variables interact across different states. Cross-sec- tions of the pVT-surface produce pT- and pV-diagrams: pT-dia- Interpret pVT-surfaces in the context of pT and pV-diagrams. grams show how pressure changes with temperature at constant volume, while pV-diagrams show how pressure changes with volume at constant temperature, providing insights into phase transitions and thermodynamic behaviors. The combination of temperature and pressure that causes a ma- Define a material's triple point. terial to technically simultaneously exist as a solid, liquid, and gas. State the equation for the work done in a volume change. W = the integral from V_1 to V_2 of pdV. U=Q W State the First Law of Thermodynamics. dU = dQ dW C_P = C_V + R State the relationships between the molar heat capacities. ³ =C_P /C_V TV^³1 =constant State the adiabatic relationships from the ideal gas law. pV^³ =constant A collection of objects that can be classified as individual units Describe a thermodynamic system. which have the potential to exchange (ex. heat pops popcorn --> increased force exerted on lid of the kettle lid). 2/4  Exam 3 Definitions and Derivations Study online at https://quizlet.com/_fy06wm Isochoric: constant volume; change in volume = 0, so w = 0. Isobaric: constant pressure; slope = 0, so the area underneath a Derive each equation for the work done in a simple thermodynam- certain section of the curve ’ W = p(V_2 - V_1). ic system across each type of thermodynamic process: isochoric, Isothermal: constant temp; change in internal energy stays con- isobaric, isothermal, and adiabatic. stant, so Q = W (first law). Adiabatic: No heat transfer in/out ’ Q = 0; -”U = W (first law). Take note of the constant variable (pressure, volume, temp, or Describe and properly interpret thermal processes on pV-dia- internal energy) and recall how to describe the work that kind of grams. process produces. If closed path on a pV diagram, then change in internal energy Know that the total internal energy change for a cyclic process is equals zero. Otherwise, some energy must've been gained or lost zero. somewhere along the way. Know that in a isolated system, there is no interaction with its Closed systems adhere to conservation of energy as defined by surroundings (Q = 0, W = 0), so U = 0. Joule. Derive the associated U , Q and W associated with each type of Change in U = W; use in conjunction with the first law, U = Q W. thermodynamic process. Q = W = Q_H = Q_C (for a cycle where U = 0). Write the formulae for the second laws of thermodynamics. S e 0. Write the equation for the thermal efficiency of a heat engine. e = W/Q_H = 1 + Q_C/Q_H Write the coefficient of performance for a refrigerator (which de- K = |Q_C|/|W| scribes its effectiveness) and its use as a heat pump. K = |Q_H|/|W| (in heating mode) State the efficiency and coefficient of performance for a Carnot e_Carnot = 1 - (T_C/T_H) engine and refrigerator, respectively. K_Carnot = T_C/(T_H - T_C) S = + dQ/T Write the definitions of entropy. S = k*ln(w) Reversible - where a process can naturally occur both forwards and backwards. Describe reversible and irreversible processes. Irreversible - where a process can only naturally occur forwards (all thermodynamic processes). A device or machine that transforms heat energy into some Recall the basic definition of a heat engine. amount of work or mechanical energy. Recall the sign conventions for Q and W as it pertains to *heat Q_H > 0, Q_C < 0, and W > 0 for expansion. engines*. Recall the sign conventions for Q and W as it pertains to *refrig- Q_H < 0, Q_C > 0, and W < 0. erators*. Recall that using absolute values in the above equations may help |Q_H| = |Q_C| + |W|. assist in maneuvering these concepts. Heat engine - converts heat to work by moving energy from a hot to a cold reservoir. Refrigerator - use work to transfer heat from a cold to a hot Recall the similarities and differences between a heat engine, a reservoir to *cool a space (cold reservoir)*. refrigerator, and a heat pump. Heat Pump - use work to transfer heat from a cold to a hot reservoir to *heat a space (hot reservoir)*. All three transfer heat energy between different temperature reservoirs. Recall efficiency is described as: Desired output/required input. 1. It is physically impossible for a system to absorb heat at some temperature, completely convert it to mechanical energy, and end Recall and explain the various statements of the 2nd law of in the same state which it began. thermodynamics. 2. It is impossible for any process to have as its sole result the transfer of heat from a cooler to a hotter object. (some work is required) 3/4  Exam 3 Definitions and Derivations Study online at https://quizlet.com/_fy06wm An ideal gas is in a container trapped by a piston on top of it: 1. The gas expands isothermally at temperature T_H, absorbing heat Q_H. 2. It expands adiabatically until its temperature drops to T_C. Recall the steps in a Carnot cycle. 3. It is compressed isothermally at T_C, rejecting heat |Q_C|. 4. It is compressed adiabatically back to its initial state at temper- ature T_H. Everything is reversible! Free Expansion - where a gas expands randomly in all directions Explain the free expansion of a gas and why it is different than in a vacuum. This is different from other processes since no work other processes. is required. Entropy - a quantifiable measure of the tendency for matter to Detail entropy and its relationship with the 2nd law of thermody- seek disorder. No matter what, an increase in entropy will always namics. accompany a naturally occurring process (increase in universal thermodynamic equilibrium). 4/4