II$.1$ kilogram of Hydrogen initially at $3$ bar and $300K,$ and $3kg$ of carbon dioxide initially at $1$ bar

and $500K,$ are confined to the opposite sides of a rigid, well insulated container. The partition is

free to move and allows conduction from one gas to the other without energy storage in the

partition itself.

Taking the system as the entire container, which of the following is true?

a$)U_{sys}=W_{in}$

b$)U_{sys}=0$

c$)U_{sys}=Q_{in}$

d$)U_{sys}=W_{in}-Q_{\text{o}\text{u}\text{t}}$

We can think of the whole container as being composed of $2$ smaller subsystems: $1$ for the

hydrogen and $1$ for the carbon dioxide. Knowing this, select the correct statement below.

a$)U_{H_2}=-U_{C{O}_2}$

b$)U_{H_2}+U_{C{O}_2}=Q_{in}$

c$)U_{H_2}+U_{C{O}_2}=W_{in}$

d$)U_{H_2}+U_{C{O}_2}=W_{in}-Q_{\text{o}\text{u}\text{t}}$

Which properties must be equal between the $C{O}_2$ and $H_2$ sides of the container once the

system reaches its final equilibrium? Select all that apply.

a$)P$

b$)v$

c$)T$

d$)u$

e$)h$

Page $1$ of $3$

Approximating the specific heat of each gas to be constant and equal to the value at $300K$

$($Table A$-2)$ for simplicity, what is the final temperature of the $C{O}_2?$

a$)332K$

b$)400K$

c$)496K$

d$)376K$

What is the final pressure of the $H_2?($Hint: The total volume of the container must remain

constant.$)$

a$)176$kPa

b$)154$kPa

c$)306$kPa

d$)224$kPa