the emission from dust species $i$ at a wavelength $\lambda$ can be estimated as $$\begin{aligned}
\mathcal{J}_\nu^i(\lambda )=
\int_{a_\mathrm{min}}^{a_\mathrm{max}}\mathrm{d}
a\frac{1}{n_\mathrm{H}}n_i(a)\pi a^2Q_\mathrm{abs}
(\lambda )\int_0^\infty\mathrm{d}T\, B_\nu (T)
\frac{\mathrm{d}P_i}{\mathrm{d}T},\hspace{-1cm}\nonumber\\\end{aligned}$$ where $B_\nu (T)$ is the Planck function at frequency $\nu$ and temperature $T$, and $\mathrm{d}P_i/\mathrm{d}T$ is the temperature distribution function of the grains under the ISRF evaluated in Section \[subsec:isrf\]. The calculation method of $\mathrm{d}P_i/\mathrm{d}T$ is based on the concept of stochastic heating, and we follow the formalism of @draine01 (see their section 4). We assume that the FIR radiation is optically thin. Thus, after the radiative transfer effect, the intensity at $\lambda$ per frequency per hydrogen nucleus per solid angle, $I_\nu (\lambda )$, becomes $$\begin{aligned}
I_\nu (\lambda)=\int_0^{s}\mathcal{J}_\nu\,\mathrm{d}s\, ,\end{aligned}$$ where $s$ is the path length, which is proportional to $A_V$. Here the colour at wavelengths of $\lambda_1$ and $\lambda_2$ is defined as $I_\nu (\lambda_1)/I_\nu (\lambda_2)$, which is called $\lambda_1-\lambda_2$ colour and denoted as $(\lambda_1/\lambda_2)_\mathrm{cl}$ (we omit $\mu$m in this expression; e.g. $(60/100)_\mathrm{cl}$ and $(140/100)_\mathrm{cl}$). Since we only consider colours (i.e. flux ratios), the proportionality constant between $s$ and $A_V$ does not matter in this paper. Thus, practically, we can replace $s$ with $A_V$.

[ Since we calculate colours in this paper, we can define the 