Specific heat capacity for adiabatic & isothermal process

[metalrose]

Can we define specific heat capacity for an adiabatic process ??

Would it always be zero since dQ is 0 for an adiabatic process?

Also, can we define specific heat capacity for isothermal processes ?
Would it be infinity in all cases?

Just want to verify if I am thinking along the correct lines.

 

[0xDEADBEEF]

The heat capacity is a property that defines how much energy is saved in a material for a given change of temperature. A definition of it will -- out of necessity -- always contain a (possibly virtual) change of temperature. In the equation of state one other variable will have to be allowed to change to keep the equation of state satisfied. You could also keep some other value constant like p+a*V.Your way of defining heat capacity doesn't look right. In an adiabatic process the gas changes temperature because the energy invested in work will go into the gas and has no time to escape. From dQ = 0 for the whole process doesn't follow anything about the gas' heat capacity.

 

[Andrew Mason]

The heat capacity is a property that defines how much energy is saved in a material for a given change of temperature.

If that was the definition, Cp and Cv would be the same. The energy saved in a gas that undergoes a certain temperature change is the same whether the temperature change occurs during expansion at constant pressure or at constant volume. But we know from the first law that this cannot be the case.

A definition of it will -- out of necessity -- always contain a (possibly virtual) change of temperature. In the equation of state one other variable will have to be allowed to change to keep the equation of state satisfied. You could also keep some other value constant like p+a*V.Your way of defining heat capacity doesn't look right. In an adiabatic process the gas changes temperature because the energy invested in work will go into the gas and has no time to escape. From dQ = 0 for the whole process doesn't follow anything about the gas' heat capacity.

The heat capacity at 0 heat flow is a rather meaningless term. It is like asking the mileage a car gets when it is standing still. If the OP wants to define what he means by heat capacity when there is 0 heat flow, perhaps we could give some meaning to the concept.