The duke´s in an audience with an emissary because he intends to marry the cout´s doughter, because of that he does his best to impress the emissary and convince he is the best choice.
During the conversation it´s infered that the Duke sent the duchese away and that´s why he wants another one.
The Duke is conversing with an emissary of a tally. The Duke is attempting to wed the check's little girl, so he is endeavoring to awe the emissary. In portraying the sketch of his latest duchess, he imparts more about himself than he does of his late spouse. He takes note of that the Duchess' look of "euphoria" in the work of art is not on the grounds that he was available amid the artistic creation.