Air undergoes a polytropic process in a piston$-$cylinder assembly from $p_1=\frac{1}{b}ar,T_1=295K$ to $p_2=\frac{3}{b}ar.$ The air is modeled as an

ideal gas and kinetic and potential energy effects are negligible.

For a polytropic exponent of $1\mathrm{.}6,$ determine the work and heat transfer, each in kJ per kg of air,

$(1)$ assuming constant $c_v$ evaluated at $300$ K $.$

$(2)$ assuming variable specific heats.