Carnot efficiency against the cold temperature

An engine's hot reservoir is at $680\ \text{K}$. You will make the program draw the best possible efficiency for cold reservoirs from $250\ \text{K}$ to $600\ \text{K}$, and compare a real engine with that limit. The real engine takes in $2300\ \text{J}$ and gives out $1520\ \text{J}$ each cycle, with its cold side at $320\ \text{K}$.

The idea. The Carnot efficiency is $\eta = 1 - \dfrac{T_c}{T_h}$. A real engine's efficiency is $1 - \dfrac{Q_c}{Q_h}$, always below the limit.

Your tasks.

1. Work out eta, the Carnot efficiency for every cold temperature in Tc.
2. Work out eta_real, the real engine's efficiency.
3. Work out eta_limit, the Carnot limit at $320\ \text{K}$, and share, the fraction of it the real engine reaches.