Answer
$Q=94.49\ kJ$
Work Step by Step
Total energy balance:
$Q-W_b=\Delta U$
For ideal gases:
$PV=mRT$
In the initial state ($P_1=100\ kPa,\ T_1=296\ K,\ V_1=0.25\ m³,\ R=0.287\ kJ/kg.K$):
Solving for the mass: $m = 0.294\ kg$
For the second state ($P_2=200\ kPa$):
Solving for the temperature: $T_2=592\ K$
$W_{b,2-3} = P_2(V_3-V_2)=mR(T_3-T_2),\ W_b{1-2}=0\ (constant\ volume)$
$W_b=W_{b,2-3}=9.12\ kJ$
$\Delta U = mc_v(T_3-T_1)$
With $c_v=0.718\ kJ/kg.K$
$\Delta U=85.37\ kJ$
Hence,
$Q=94.49\ kJ$
