# Air-standard Power Cycles

UNDER CONSTRUCTION
This is a topic from Thermodynamics:

## Introduction

A basic understanding of various forms of thermodynamic cycles is necessary for solving thermodynamic problems of a practical nature.

## The Compression Ratio

For certain piston cycles, where there is a swept and clearance volume, the compression ratio is defined as:

rv = (Vswept + Vclearance) / Vclearance

## The Air-Standard "Otto" Cycle

The cycle is as follows:

1→2: Isentropic compression
3→4: Isentropic expansion

The Otto cycle on a PV diagram: Analysis:

• The volume in states 2 and 3 is the 'clearance' volume, such that the piston is almost at the top of the cylinder
• The volume in states 1 and 4 is the 'swept' volume , such that the piston is as far down the cylinder as it reaches during the cycle
• The work done for the isochoric processes (2→3 and 4→1) is equal to zero, and so by the first law: :::QH = m(u3/1 - u2/4) = mCV(T3/1 - T2/4)
• Recalling the definition of engine efficiency:
ηth = Wnet / Qin = (QH - QL) / QH,
ηth = (mCV(T3 - T2) - mCV(T4 - T1))/mCV(T3 - T2) = ((T3 - T2) - (T4 - T1)) / (T3 - T2)
• And so:
ηth = 1 - ((T4 - T1) / (T3 - T2)
T2 / T1 = (v1/v2)k-1 and T3 / T4 = (v2/v3)k-1, and so
T2 / T1 = T3 / T4
• The compression ratio here would be given by:
rv = v1/v2
• And thus the expression for efficiency can be rewritten:
ηth = 1 - T1 / T2 = 1 - rv1-k
...we can see therefore, that increasing the compression ratio is best for efficiency.