Chapter 3, Problem 3.3NP

Interpretation Introduction

Interpretation:

The value of q, w, ΔU and H needs to be determined for the given conditions considering ideal gas behavior for the matter.

Concept Introduction:

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

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

From first law of thermodynamics, the enthalpy of system is obtained as:

  $H=U+PV$

The energy (q) of a system is obtained as:

  $\begin{array}{c}\Delta U=q+W\\ q=\Delta U+W\\ W=\Delta U-q\\ \text{Since, workdone in terms of pressure is obtained as }\\ dW=PdV\\ dU=dq-PdV\end{array}$

Putting the equations together; (at constant pressure)

  $\begin{array}{c}\Delta H=\Delta U+\Delta (PV)\\ \Delta H=\Delta q-P\Delta V+P\Delta V\\ \Delta H=\Delta q\\ H=q\end{array}$

Hence, in the given case value of $\Delta$ H and q will be same.

The enthalpy change is also obtained as:

  $\begin{array}{l}\Delta \text{H}=\text{n}{\displaystyle \underset{{\text{T}}_{\text{i}}}{\overset{{\text{T}}_{\text{f}}}{\int }}{\text{C}}_{\text{p,m}}\text{dT}}\text{, }\\ {\text{where n= mole, C}}_{\text{p}\text{.m}}\text{ = molar specific heat, dT= change in temperature, }\\ {\text{T}}_{\text{i}}{\text{=Initial temperature, and T}}_{\text{f}}\text{=Final temperature}\end{array}$