Lecture 43 Heat engine and efficiency Reversible and irreversible processes Heat engines

Irreversible process A process that is not reversible is called irreversible. An irreversible process is a process that the thermodynamic state of the system and all of its surroundings cannot be precisely restored to its initial state without expenditure of energy. Example: free expansion

Reversible processes A reversible process is a process that the thermodynamic state of the system and all of its surroundings can be precisely restored to its initial state by infinitesimal changes in some property of the system without expenditure of energy. Due to these infinitesimal changes, the system is in thermodynamic equilibrium throughout the entire process. Reversible processes are always quasistatic, but the converse is not always true. friction between the system and its surroundings.

Thermodynamic cycle A thermodynamic cycle consists of a linked sequence of thermodynamic processes that involve transfer of heat and work into and out of the system, while varying pressure, temperature, and other state variables within the system, and that eventually returns the system to its initial state. V p

𝑾 The work done by the process 𝑊= 𝑝𝑑𝑉 Heat transferred into the system V p The work done by the process 𝑊= 𝑝𝑑𝑉 Heat transferred into the system 𝑄= 𝑄 𝑖𝑛 − 𝑄 𝑜𝑢𝑡 For the system returns to its initial state the first law of thermodynamics applies Δ 𝐸 𝑖𝑛𝑡 =0 So 𝑊=𝑄 If the cyclic process moves clockwise around the loop, then W will be positive, and it represents a heat engine. If it moves counterclockwise, then 𝑊 will be negative, and it represents a heat pump. 𝑾

Efficiency of a heat engine The efficiency of a heat engine relates how much useful work is output for a given amount of heat energy input. Δ𝑊=Δ 𝑄 ℎ +Δ 𝑄 𝑐 Δ 𝑄 ℎ is the heat energy taken from the high temperature system. (It is positive since heat is extracted from the source.) Δ 𝑄 𝑐 is the heat energy delivered to the cold temperature system. (It is negative since heat is added to the sink.) The efficiency is defined as 𝜂= Δ𝑊 Δ 𝑄 ℎ = Δ 𝑄 ℎ +Δ 𝑄 𝑐 Δ 𝑄 ℎ =1− Δ 𝑄 𝑐 Δ 𝑄 ℎ Is it possible to find a process to make 𝜂=1?

The internal-combustion engine A fuel vapor can be compressed, then detonated to rebound the cylinder, doing useful work.

The Otto cycle An Otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. 𝜂= Δ𝑊 Δ 𝑄 ℎ = Δ 𝑄 ℎ +Δ 𝑄 𝑐 Δ 𝑄 ℎ =1− Δ 𝑄 𝑐 Δ 𝑄 ℎ Δ 𝑄 𝑐 = 𝐶 𝑉 𝑇 𝑑 − 𝑇 𝑎 Δ 𝑄 ℎ = 𝐶 𝑉 ( 𝑇 𝑐 − 𝑇 𝑏 ) 𝜂=1− 𝑇 𝑑 − 𝑇 𝑎 𝑇 𝑐 − 𝑇 𝑏 =1− 𝑇 𝑎 𝑇 𝑏 𝑇 𝑑 𝑇 𝑎 −1 𝑇 𝑐 𝑇 𝑏 −1 𝑝 𝑏 𝑇 𝑏 = 𝑝 𝑐 𝑇 𝑐 , 𝑝 𝑑 𝑇 𝑑 = 𝑝 𝑎 𝑇 𝑎 → 𝑇 𝑐 𝑇 𝑏 = 𝑝 𝑐 𝑝 𝑏 , 𝑇 𝑑 𝑇 𝑎 = 𝑝 𝑑 𝑝 𝑎 𝑝 𝑐 𝑉 𝑐𝑏 𝛾 = 𝑝 𝑑 𝑉 𝑎𝑑 𝛾 , 𝑝 𝑏 𝑉 𝑐𝑏 𝛾 = 𝑝 𝑎 𝑉 𝑎𝑑 𝛾 𝑝 𝑐 / 𝑝 𝑏 = 𝑝 𝑑 / 𝑝 𝑎 𝜂=1− 𝑇 𝑎 𝑇 𝑏

Stirling engine Isothermal expansion. Isochoric (constant-volume heat removal) Isothermal compression Isochoric (constant-volume heat addition) Thermal Expansion and Contraction For 𝑄 4 =− 𝑄 2 , define 𝜂= 𝑄 1 −| 𝑄 3 | 𝑄 1 =1− 𝑄 3 𝑄 1 𝑄 1 = 𝑊 1 =𝑛𝑅 𝑇 1 ln 𝑉 2 𝑉 4 𝑄 3 = 𝑊 3 =𝑛𝑅 𝑇 3 ln 𝑉 4 𝑉 2 𝜂=1− 𝑇 3 𝑇 1

斯特林发动机

Actual performance

California Edison 25 kW dish/Stirling system California Edison 25 kW dish/Stirling system. The 944 square foot concentrator consists of 82 spherically curved glass mirrors each 3 foot by 4 foot. The United Stirling 4-95 Mark II engine (4 cylinders of 95 cc displacement) uses hydrogen as the working pressure at a maximum gas pressure of 2900psi.. This engine delivered 25kW output at 1000W/m2 insolation.