Q:

How Heat is constant in adiabatic process

Consider adiabatic cylinder with a piston attached. $Q=0$ in this case and Work done is equal to change in internal energy. If I do work on the piston then its internal energy increases and so its heat because heat is the measure of internal energy of ideal gas. So how we say heat is constant in adiabatic process?

A:

The concept of heat can be quite tricky.  Your cylinder and piston are a system and everything outside the system are the surroundings.  The system has internal energy which is the sum of the kinetic energy and the potential energy of all the molecules which make up the system.  There are two processes by which energy can flow in or out of the system.  One is called working and the other is heating.
If you have an adiabatic change that means that no heat can flow in or out of the system.
Your mistake is to think that because the temperature of the system has increased the amount of heat the system has got has also increased.  That is not true.  The concept that a system has heat stored inside itself is wrong.  The fact that the average kinetic energy of the molecules has increased ie the temperature of the system has increased does not mean that the system has more heat inside it.  In the case of an adiabatic change that increase in internal energy must have been as a result of work being done on the system.

