Chapter 2, Problem 2.1NP

Interpretation Introduction

Interpretation:

The workdone during the compression of gas and the distance travelled by the piston should be calculated in the given process assuming that the mass of piston is negligible.

Concept Introduction:

The ideal gas equation is used to find out the volume of any gas produced under given conditions as follows:

  $\begin{array}{l}\text{PV=nRT}\\ \text{Where, P= Pressure, V=volume, n= number of moles, R= universal gas constant and T= temperature}\end{array}$

Pressure is force applied per unit area. The external force in adiabatic compression is calculated as a sum of internal force and force applied by piston as follows:

  $\begin{array}{c}{\text{P}}_{Ext}{\text{=P}}_i\text{ + }\frac{F}{A}\\ ={\text{P}}_i\text{ + }\frac{mg}{\pi r^2}\\ {\text{Where, P}}_i\text{= Internal Pressure, m=mass of gas, g= accelartion due to gravity= 9}{\text{.8m/s}}^2\text{, r= radius of piston}\end{array}$

In case of ideal gases: the change in internal energy is obtained as:

  ${\text{ΔU=nC}}_{\text{v,m}}{\text{ΔT, where n= mole, C}}_{v.m}\text{ = molar specific heat and }\Delta \text{T= change in temperature}$

Similarly, work done by the system is calculated as:

  ${\text{W= -P}}_{\text{Ext}}{\text{ΔV where, P}}_{Ext}\text{ is external pressure and }\Delta \text{V is change in volume}\text{.}$