Speed of a process in thermodynamics As per my understanding, all adiabatic processes carried out in absence of an adiabatic wall need to be fast enough so that there is no heat exchange with the surrounding. Similarly, all isothermal processes are slow so that thermal equilibrium can be established with the surroundings in order to maintain a constant temperature in the system. 
But then since isothermal processes are slow, how are isothermal irreversible processes possible? 
Is my notion that 'irreversible processes are fast' wrong? 
 A: There are some irreversible processes that can be slow.  However, when we refer to an isothermal irreversible process, what we really mean is that the boundary of the system with its surroundings are maintained at a constant temperature during the process, even if the process is fast.  So, although the temperature at the boundary is constant, the temperature distribution within the system is not spatially uniform, and irreversible heat conduction is occurring within the system.  Also, typically in an isothermal irreversible process, the boundary temperature is assumed to be held at the initial uniform temperature of the system in its initial thermodynamic equilibrium state, and the temperature of the system again becomes uniform at the boundary temperature in the final equilibrium state of the system.
A: Thermodynamics doesn't deal with rate or speed. Instead it deals only with initial state and final state, or a series of states. Mostly, it likes a very very slow process. Anything fast will generate result deviating from the thermodynamics solution. 
When you talk about a fast process. It is true there is no time for heat to transfer though there still be some. However, when it is a fast movement of piston in a chamber, the gas in the chamber is not uniformly distributed, neither temperature nor concentration. There is no way you can use thermodynamics laws to get the distribution. 
So, all what we said is "fast" indicates adiabatic. And it is a good approximation in real life. But don't forget we have another assumption that the internal system mixes very well, which usually needs a slow process to achieve. 
