Answer
$R=2.075\ kJ/kg.K$
$M=4.007\ kg/kmol$
$c_v=3.111\ kJ/kg.K$
$c_p=5.186\ kJ/kg.K$
Work Step by Step
Since for a constant-pressure process on an ideal gas:
$W_b=mR\Delta T$
Given $W_b=16.6\ kJ,\ m=0.8\ kg,\ \Delta T=10K$
solving for R: $R=2.075\ kJ/kg.K$
Since:
$R_u=8.314\ kJ/kmol.K=R.M$
$M=4.007\ kg/kmol$
For ideal gases :
$c_v=\frac{R}{k-1}$
With $k=1.66$:
$c_v=3.111\ kJ/kg.K$
Since:
$c_p=c_v+R$
$c_p=5.186\ kJ/kg.K$
