Chapter 2, Problem 2.35NP

(a)

Interpretation Introduction

Interpretation: The final temperature for the adiabatic expansion of 0.5 mol of an ideal gas with $C_{V,m}$ =3R/2. The initial pressure and temperature is 6.25 bar and 300 K respectively. Also, the final pressure is 1.25 bar.

Concept Introduction: For an adiabatic process, the heat involved is equal to zero. The molar heat capacity at constant volume is represented as $C_{V,m}$ and molar heat capacity at constant pressure is $C_{P,m}$ .

(b)

Interpretation Introduction

Interpretation: The final temperature needs to be determined, if the same gas undergoes adiabatic expansion with external and final pressure equals to 1.25 bar.

Concept Introduction: The change in internal energy is calculated as follows:

  $\Delta U=n{C}_{V.m}\left(T_f-T_i\right)$

Here, n is number of moles, $C_{V,m}$ is molar heat at constant volume and T is temperature.

The work done is represented as follows:

  $w=-P_{\text{external}}\Delta V$

Here, P is external pressure and $\Delta V$ is change in volume.

The enthalpy of a reaction is represented as follows:

  $\Delta H=\Delta U+nR\Delta T$

Here, n is number of moles, R is Universal gas constant and $\Delta T$ is change in temperature.