Since $P{V}^{\text{n}}=$ constant and also $PV=RT$, taking $1 \mathrm{mol}$ of the gas for simplicity,

        $\text{d}\mathit{\text{U}}={\mathit{\text{C}}}_{\text{v}}\text{d}\mathit{\text{T}}$

where $C_{\text{v}}\to$ molar specific heat at constant volume.
Now the molar specific heat in a polytropic process ${\mathit{\text{PV}}}^{\text{n}}=$ constant is given by

         $C=\left(\frac{R}{\gamma -1}\right)-\left(\frac{R}{\text{n}-1}\right)=\frac{\left(\text{n}-\gamma \right)R}{\left(\text{n}-1\right)\left(\gamma -1\right)}$               ...(i)

From this equation, we see that C will be negative when $\text{n}<\gamma$ and n > 1, simultaneously, i.e., $1<\text{n}<\gamma$. Since $\gamma$ for all ideal gases is greater than 1, if $\text{n}>\gamma$ or $\mathrm{n} < 1$, then C_v will be positive.