Answer
(a) $\Delta U = 747 J$
(b) $\gamma = 1.30 $
Work Step by Step
(a) Change of internal energy
$\Delta U = Q - W$
$\Delta U = 970 J - 223 J $
$\Delta U = 747 J$
(b) To calculate the $\gamma$ we need to identify the $C_p$ and $C_V$
$C_p = \frac{Q}{n \Delta T} $
$C_p = \frac{970 J }{(1.75 mol) (15.0 K)} $
$C_p = 37.0 J/mol.K$
$C_V = \frac{\Delta U}{n \Delta T} $
$C_V = \frac{747 J }{(1.75 mol) (15.0 K)} $
$C_V = 28.5 J/mol.K $
$\gamma = \frac{c_p}{c_V} $
$\gamma = \frac{37.0 J/mol.K}{28.5 J/mol.K} $
$\gamma = 1.30 $
