Heat transfer with surroundings: why considered reversible? I do not understand how the fact that the surroundings are large makes heat transfer with them reversible? I understand that the temperature of the surroundings is not going to change in the limit, but what about processes in which there is a definite temperature gradient with the system, such as a highly exothermic reaction? 

I was sure that this question had already been asked somewhere on Stack, but I can't find anything similar – if you know of one, I would really appreciate if you could refer me to it.
The surroundings are typically modelled in thermodynamics as an ideal (reversible) reservoir with infinite heat capacity and negligible temperature gradients (i.e., infinite thermal conductivity).  The assumption is that the temperature gradients are confined to the system, rather than the surroundings, and the entropy generation is confined to the system.  Of course, in real life, this is only an approximation.