Heat Capacity at constant volume:
CV = (partial q / partial T) with V constant
since volume is constant, work is zero and dq = dU, so
CV = (partial U / partial T) with V constant
Delta U = CV * Delta T
Does this final relationship hold during a reaction where volume is NOT constant? Why or why not?
No, the final relationship ΔU = CV * ΔT does not hold during a reaction where the volume is not constant. This is because the heat capacity at constant volume (CV) is defined specifically for systems where the volume is held constant. In such systems, there is no work done because no volume change occurs, and therefore the change in internal energy (ΔU) is equal to the heat added or removed (ΔQ).
However, when the volume is not constant, work is involved in addition to heat transfer. In such cases, the change in internal energy (ΔU) is given by the equation:
ΔU = ΔQ - ΔW
Here, ΔQ represents the heat added or removed, and ΔW represents the work done on or by the system. Since work is involved, the heat capacity at constant volume (CV) alone cannot be used to calculate the change in internal energy.
To consider a reaction where volume is not constant, you would need to take into account the appropriate heat capacity. For example, if the volume is changing, you would use the heat capacity at constant pressure (CP) instead, which accounts for the work done during the process.
The relationship between the change in internal energy (ΔU) and heat capacity at constant pressure (CP) can be expressed as:
ΔU = CP * ΔT
So, when the volume is not constant, you would use the heat capacity at constant pressure (CP) to calculate the change in internal energy.