Chapter 3, Problem 3.38P

Interpretation Introduction

Interpretation:

The values of $T_A$, $T_B$ and $Q/n_A$ after heating should be calculated, given that a frictionless floating piston divides the cylinder into two sections $A$ and $B$ . The heating element in section $A$ increases temperature and in section $B$, temperature increases because of adiabatic compression.

Concept Introduction:

The value of $T_B$ can be calculated using adiabatic compression relation between temperature and pressure. For adiabatic compression from $t=0$ to $t=t$ :

  $T_B=T_1{(\frac{P_2}{P_1})}^{\raisebox{1ex}{$\gamma -1$}\!\left/ \!\raisebox{-1ex}{$\gamma $}\right.}$

Where $T_B$ is temperature of section $B$ after the heating or $t=t$, $T_1$ is temperature of section $B$ before the heating or $t=0$, $P_2$ is pressure of cylinder after the heating or $t=t$, $P_1$ is pressure of cylinder before the heating or $t=0$

For $T_A$, Since it is given that two sections contain equal mass of air, hence number of moles before the heating and after the heating will be same or we can say total volume is constant. So,

  $n_1=n_2\text{and }{n}_A=n_B$

Where $n_1$ is the number of moles in cylinder having two sections before heating and $n_2$ is the number of moles in cylinder having two sections after heating.