Answer
$\Delta S = 8.64 J/K$
Work Step by Step
The equation of entropy in thermodynamics is
$\Delta S = nC_V ln (\frac{T_c}{T_b})$ and $C_V = \frac{3}{2} R$
Taking from (b), $T_b = \frac{4.0p_oV_o }{nR} $ and $T_c = \frac{8.0p_oV_o }{nR}$. Substitute into entropy equation
$\Delta S = n(\frac{3}{2} R) ln (\frac{\frac{8.0p_oV_o }{nR}}{\frac{4.0p_oV_o }{nR}})$
$\Delta S = n(\frac{3}{2} R) ln (\frac{8.0}{4.0})$
$\Delta S = (1)\frac{3}{2} (8.31 J/K) ln (2)$
$\Delta S = 8.64 J/K$
