The Laws of Thermodynamics - Introductory Physics I | PHY 231, Study notes of Physics

Download The Laws of Thermodynamics - Introductory Physics I | PHY 231 and more Study notes Physics in PDF only on Docsity! 1 Chapter 12: The laws of Thermodynamics Work in thermodynamic processes The work done on a gas in a cylinder is directly proportional to the force and the displacement. yPAyFW Δ−=Δ−= VPW Δ−= It can be also expressed in terms of the pressure excerted by the piston and the variation in volume. Compression: work is positive Expansion: work is negative 2 Work: questions A monoatomic gas is expanded from an initial state with volume V=1 l to a final state 4V. This process happens at constant pressure P=1 atm. Next, the pressure on the gas is increased at constant volume 4V. 1) The work done during the first process is: a) positive, b) negative c) zero 2) The work done during the second process is: a) positive, b) negative c) zero 3) What is the net work and sketch the processes in a graph of P versus V. PV diagrams The work done on a gas when taking it from an initial thermodynamic state (I) to a final thermodynamic state (f) can be determined by the area below the PV diagram. 5 First law of thermodynamics: question Which of the following processes correspond to 1. Isobaric 2. Isothermal 3. Isovolumetric 4. Adiabatic First law of thermodynamics: example An ideal mono-atomic gas is confined in a cylinder by a movable piston. The gas starts at P=1.00atm, V=5.00L and T=300K. An isovolumetric process raises the pressure to 3 atm. Then an isothermal expansion brings the system back to 1atm. Finally an isobaric compression at 1atm completes the cycle and return the gas to its original state. 1) Find the number of moles, the temperature B, and the volume of the gas at C. 6 First law of Thermodynamics: example 2) Find the internal energy of the gas, at A, B, and C. List P,V,T, U for the points A,B and C. 3) Consider the process A to B, B to C and C to A. For each case determine the sign of W and Q. 4) Calculate Q, W and ΔU for each transition 5) Tabulate W,Q and ΔU for each transition and calculate the net effect of each. Heat engines The heat engine is a device that converts internal energy into other useful forms of energy (electrical, mechanical, etc) In general, it carries a working substance (ex: water) through cycles: 1) Energy is transferred from a hot reservoir 2) Work is done by the engine 3) Energy is expelled into a cold reservoir 7 Heat engines Because the substance goes through a cycle its initial internal energy is the same as the final: |||| coldhotengine netengine QQW QW −= −= The work done by an engine for a cyclic process is the area enclosed in the curve of a PV diagram Thermal efficiency of Heat engines Thermal efficiency of the heat engine is the ratio of the work done by the engine to the energy absorbed from the hot reservoir in a cycle || ||1 || |||| || hot cold hot coldhot hot eng Q Q Q QQ Q W −= − = = ε ε Second law of thermodynamics: It is impossible to construct a heat engine with 100% efficiency! 10 Heat engines: example A car engine delivers 8.2 KJ of work per cycle. a) Before tune-up the efficiency is 25%. Calculate, per cycle, the heat absorbed from combustion of fuel and the energy lost by the engine b) After a tune-up the efficiency is 31%. What are the new values of the quantities calculated in a) when 8.2 KJ of work is delivered per cycle. Human metabolism The metabolic rate is proportional to the consumption of oxygen by volume t V t U O Δ Δ = Δ Δ 28.4 11 Efficiency Human body as a machine The metabolic rate is related to the rate at which work is done and heat if transferred t W t Q t U Δ + Δ = Δ Δ The efficiency of the human body is the ratio between the work rate and the metabolic rate t U t W Δ Δ Δ=ε Efficiency Human body as a machine 12 Entropy Entropy (S) is a measure of the state of disorder of a system T QS r=Δ Second law of thermodynamics: the entropy of the universe increases in all natural processes. The change in Entropy (S) of a system between two equilibrium states is given by the energy transferred in a reversible path divided by the absolute temperature T of the system in this interval Entropy: question time Which of the following statement is true for a reversible, adiabatic path: a) ΔS=0 b) ΔS>0 c) ΔS<0 Two gases A and B are initially in contact with a hot source at temperature T. The heat exchanged to A is twice the heat transferred to B. What can you conclude about their change in entropy ΔS? What can you say about their absolute state of disorder?