Heat transfer confusion suppose two objects are at 0 degree celcius
if they are heated uptil both temperature reach  20 degree celcius
so their specific heat capacity is different,so they will absorb different amount of heat but their temperature would be same,
so in this case if both the objects are in contact ,will heat exchange happen,because both have same same temperature so they should not,but both have different heat energy levels so heat moves from higher energy potential to lower potential level//
 A: No. Heat is the transfer of thermal energy between objects that have different temperatures regardless of their conditions. Thermal energy always moves from an object with a higher temperature to an object with a lower temperature.
This is a statement of the second law of thermodynamics where this law states that it is impossible for any process to have as its sole result heat transfer from a cooler to a hotter object. While from a hotter object to a cooler one, heat transfer can happen spontaneously. The natural conclusion is that for two bodies at the same temperature, no heat transfer will occur spontaneously.
A: 
so in this case if both the objects are in contact ,will heat exchange
happen

No.
Heat is energy transfer due solely to temperature difference. If there is no temperature difference between objects there can be no energy transfer in the form of heat.
I think the underlying reason for your question is not understanding the difference between heat and internal energy. The energy each of your two objects possess is its internal energy. The internal energy is the sum of the kinetic and potential energies of the molecules and atoms at the microscopic level. Heat is only the transfer of energy.
Bottom Line: Objects don't "possess" heat. After energy is transferred to or from an object in the form of heat, the increase or decrease in the energy of the object is no longer recognizable as heat. It is an increase or decrease in the internal energy of the object.
Hope this helps.
A: Heat transfer is temperature based. Heat always flows from a warmer to a cooler environment. When the two objects are at the same temperature they are at equilibrium and one cannot raise or lower the temperature of the other, no matter how much or how little energy it took to raise the temperature of each individual object from 0C to 20C.
A: 
so in this case if both the objects are in contact , will heat exchange
happen

No.
Heat is energy transfer due solely to temperature difference. If there is no temperature difference between objects there can be no energy transfer in the form of heat.

but both have different heat energy levels so heat moves from higher
energy potential to lower potential level

Heat does not move from a higher energy object to a lower energy object. Heat moves from a higher temperature object to a lower temperature object. The temperature of an object does not equal the energy of an object. Temperature is a measure of the average translational kinetic energy of the molecules of an object. The total molecular kinetic energy of the object is the average per molecule times the total number of molecules (mass of the object).
Don't think of the heat capacity of an object as a measure of how much heat is "contained" in an object. Objects don't contain heat. They contain internal energy. Heat is energy transfer due solely to temperature difference.
The heat capacity of an object determines, all other things being equal, how much the temperature of an object will change as a result of heat transfer. It also determines how much energy is available to transfer in the form of heat. The heat capacity of an object equals the specific heat of the material of the object times its mass.
As an example, suppose we have two objects A and B made of the same material (same specific heat $c$), but object B has ten times the mass of object A, meaning it has ten times the heat capacity of A.
Let the initial temperatures be $T_{A}=200 C$ and $T_{B}=100 C$.  We place the objects in contact with one another and isolate them from everything else. Since $T_{A}>T_B$ energy will transfer in the form of heat from A to B  until they are in thermal equilibrium with each other at some final equilibrium temperature, $T_F$.
For conservation of energy, the energy lost by A if the form of heat = Energy gained by B in the form of heat.
$$mc(T_{A}-T_{F})=10mc(T_{F}-T_B)$$
$$T_{F}=108 C$$
Note that the final temperature of the two objects is much closer to the initial temperature of object B than object A. This is because the heat capacity of B is 10 times that of A. If the two objects had the same mass (same heat capacity), the final temperature would be the average of the initial temperatures.
Hope this helps.
