Since $P{V}^n=$ 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 capacity in a polytropic process $P{V}^n=$ constant is given by
         $C=\left(\frac{R}{\gamma -1}\right)-\left(\frac{R}{n-1}\right)=\frac{\left(n-\gamma \right)R}{\left(n-1\right)\left(\gamma -1\right)}$               ...(i)
From this equation, we see that C will be negative when $n<\gamma$ and

$n$  > 1, simultaneously, i.e., $1<n<\gamma$. Since $\gamma$ for all ideal gases is greater than 1, if $n>\gamma$ or $\mathrm{n} < 1$, then C_v will be positive.