Chapter 2, Problem 2.90E

Interpretation Introduction

Interpretation:

Consider a gas undergoing a reversible, adiabatic change in volume. Such changes are not isothermal, but you can still use equation 2.49. The final pressure of 1.00 mole of ideal gas at 1.00 bar initial pressure as the volume increases is to be plotted. The isothermal final pressure as volume increases from the same initial conditions (that is, Boyle’s law) is to be plotted. These two plots are to be compared.

Concept introduction:

Generally, Adiabatic process is defined as a process in which the enthalpy or heat content of the system remains constant. This process is highly useful in explaining the first law of thermodynamics. In other words, time is limited for the transfer of energy as heat has to take in and out from the system. In this process q = 0. Thus, in a given system, the enthalpy and internal energy are governed by state variables of the system. Intriguingly, the molar heat capacities of gaseous systems are determined at constant volume and can be expressed as

$\mathrm{C}\mathrm{v}\mathrm{ }=\mathrm{ }(\mathrm{\delta }\mathrm{U}/\mathrm{ }\mathrm{\delta }\mathrm{T})\mathrm{v}$