Thermodynamic Cycle Efficiency and Adiabatic Constant · USAPhO 2012 #A2
Physics · thermodynamics
Problem
An ideal (but not necessarily perfect monatomic) gas undergoes the following cycle.
• The gas starts at pressure P₀, volume V₀ and temperature T₀.
• The gas is heated at constant volume to a pressure αP₀, where α > 1.
• The gas is then allowed to expand adiabatically (no heat is transferred to or from the gas) to pressure P₀
• The gas is cooled at constant pressure back to the original state.
The adiabatic constant γ is defined in terms of the specific heat at constant pressure Cp and the specific heat at constant volume Cv by the ratio γ = Cp/Cv.
a. Determine the efficiency of this cycle in terms of α and the adiabatic constant γ. As a reminder, efficiency is defined as the ratio of work out divided by heat in.
b. A lab worker makes measurements of the temperature and pressure of the gas during the adiabatic process. The results, in terms of T₀ and P₀ are
Pressure units of P₀ | 1.21 | 1.41 | 1.59 | 1.73 | 2.14
Temperature units of T₀ | 2.11 | 2.21 | 2.28 | 2.34 | 2.49
Plot an appropriate graph from this data that can be used to determine the adiabatic constant.
c. What is γ for this gas?