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An ideal gas, initially at $30C$ and $100$kPa, undergoes the following process:

It is first compressed adiabatically to $550$kPa, then cooled at a constant pressure of $550$kPa to $30C,$ and finally

expanded isothermally to its original state.

Take $C_P=(\frac{7}{2})R$ and $C_V=(\frac{5}{2})R.$

The values of the ideal gas constant $(R)$ are given below.

NOTE: This is a multi$-$part question. Once an answer is submitted, you will be unable to return to this part.

Values of the Universal Gas Constant

$R=8\mathrm{.}314J*mo{l}^{-1}*K^{-1}=8\mathrm{.}314m^3*Pa*mo{l}^{-1}*K^{-1}$

$=83\mathrm{.}14c{m}^3\frac{*}{b}ar*mo{l}^{-1}*K^{-1}=8314c{m}^3*kPa*mo{l}^{-1}*K^{-1}$

$=82\mathrm{.}06c{m}^3*(atm)*mo{l}^{-1}{K}^{-1}=62,356c{m}^3*(torr)*mo{l}^{-1}*K^{-1}$

$=1\mathrm{.}987(cal)*mo{l}^{-1}*K^{-1}=1\mathrm{.}986(Btu)(lbmole{)}^{-1}(R{)}^{-1}$

$=0\mathrm{.}7302(ft{)}^3(atm)(lbmol{)}^{-1}(R{)}^{-1}=10\mathrm{.}73(ft{)}^3(a)(lbmol{)}^{-1}(R{)}^{-1}$

$=1545(ft)(l{b}_f)(lbmol{)}^{-1}(R{)}^{-1}$

Calculate $Q,W,U,$ and $H$ for the complete cycle considering the following condition.

Consider a mechanically reversible process.

The heat required $(Q)$ is

J$.mo{l}^{-1}.$

The work done $(W)$ is

$J*mo{l}^{-1}.$

The change in internal energy is

$J*mo{l}^{-1}.$

The change in enthalpy $(H)$ is

$J*mo{l}^{-1}.$