Describe construction and working of a heat engine with help of a labelled diagram and derive an expression for it efficiency
Answers
Carnot engine is a theoretical thermodynamic cycle proposed by Leonard Carnot. It gives the estimate of the maximum possible efficiency that a heat engine during the conversion process of heat into work and conversely, working between two reservoirs, can possess. In this section, we will learn about Carnot cycle in detail.
Carnot Engine
For an ideal gas operating inside a Carnot cycle, following are the steps involved:
Step 1: Isothermal expansion: The gas is taken from P1, V1, T1 to P2, V2, T2. Heat Q1 is absorbed from the reservoir at temperature T1. Since the expansion is isothermal, the total change in internal energy is zero and the heat absorbed by the gas is equal to the work done by the gas on the environment, which is given as:
W1→2=Q1=μ×R×T1×lnv2v1
Step 2: Adiabatic expansion: The gas expands adiabatically from P2, V2, T1 to P3, V3, T2. Here work done by the gas is given by
W2→3=μRγ−1(T1−T2)
Step 3: Isothermal compression: The gas is compressed isothermally from the state (P3, V3, T2) to (P4, V4, T2).
Here, the work done on the gas by the environment is given by
W3→4=μRT2lnv3v4
Step 4: Adiabatic compression: The gas is compressed adiabatically from the state (P4, V4, T2) to (P1, V1, T1).
Here, the work done on the gas by the environment is given by:
W4→1=μRγ−1(T1−T2)
Thermodynamic Engine..
Hence, the total work done by the gas on the environment in one complete cycle is given by:
W=W1→2+W2→3+W3→4+W4→1W=μRT1lnv2v1−μRT2lnv3v4
Netefficiency=NetworkdonebythegasHeatabsorbedbythegas
Netefficiency=WQ1=Q1−Q2Q1=1−Q2Q1=1−T2T1lnv3v4lnv2v1
Since the step 2–>3 is an adiabatic process, we can write T1V2Ƴ-1 = T2V3Ƴ-1
Or,
v2v3=(T2T1)1γ−1
Similarly, for the process 4–>1, we can write
v1v2=(T2T1)1γ−1
This implies,
v2v3=v1v2
So, the expression for net efficiency of carnot engine reduces to:
Netefficiency=1−T2T1
Carnot Theorem – As per the this theorem, any system working between two given temperatures T1(hot reservoir) and T2 (cold reservoir), can never have an efficiency more than the Carnot engine working between the same reservoirs respectively. Also, the efficiency of this type of engine is independent of the nature of the working substance and is only dependent on the temperature of the hot and cold reservoirs.
Answer:
In thermodynamics and engineering, a heat engine is a system that converts heat energy to mechanical energy, which is used to do mechanical work. It is done by bringing a working substance from a higher state temperature to a lower state temperature.
Explanation:
A heat engine is a system that converts heat into work by taking heat from the reservoir to carry out some work. There is a discharge of some heat to the sink. There are different types of heat engines from which a Carnot engine has maximum efficiency.
Working of Heat Engine
A heat engine contains a heat reservoir, an engine, and a cold sink. The heat that we produce as internal combustion or external combustion is given to the engine where the piston movement takes place. The power generated is given to the machine that is connected to the engine and hence the work is done. Excess heat is given to the sink where the temperature will remain the same at both the reservoir and sink.
Heat engines like automobile engines operated cyclically. They will add energy in the form of heat in one part of the cycle and use this energy to do work from another part of the cycle.