Problem $3.$ Two tanks are connected as shown below. Tank $1$ initially contains an ideal

gas at $10$ bar and $20C,$ and both parts of Tank $2$ contain the same gas at $1$ bar and $20$

$C.$ The valve connecting the two tanks is opened long enough to allow the pressures

in the tanks to equilibrate and then shut. There is no transfer of heat from the gas to

the tanks or frictionless piston and the constant pressure heat capacity of the gas is $4$R$.$

Write the total mass and energy balances for a$)$ the gas in subsystem $3,$ b$)$ subsystems

$2$ and $3,$ c$)$ subsystems $1$ and $2,$ including valve, d$)$ subsystem $2,$ including valve, e$)$

subsystem $1,$ including valve, and f$)$ subsystems $1,2,3,$ including valve. $($just need mass and equation balance equation and their final forms, no need for mathematical calculation$)$