abdossamad2003
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Why is this equation (red sign) written in constant volume and not in constant pressure?
The discussion centers on the use of constant volume in the adiabatic equation for internal energy of an ideal gas. Participants assert that internal energy is solely dependent on temperature, not volume, and that in adiabatic processes, the work done is zero, leading to no change in internal energy. The heat capacity at constant volume (C_V) is emphasized as a critical factor in understanding these relationships. The consensus is that the internal energy should not be considered in constant volume if the process is not truly at constant volume.
PREREQUISITESStudents and professionals in thermodynamics, physicists, and engineers seeking to deepen their understanding of internal energy and its behavior in adiabatic processes.
This is totally incorrect. Irrespective of the process, the internal energy of an ideal gas depends only on temperature, and not volume.abdossamad2003 said:The effect of volume on the internal energy is meaningful only in diabatic processes, for example, when heat is added to the system at a constant volume and the internal energy increases, but in adiabatic processes, when the volume is constant, the work done on the system is zero and the incoming heat is zero, as a result of the change in energy Internal is zero.
See, e.g., here: https://en.wikipedia.org/wiki/Internal_energy#Internal_energy_of_the_ideal_gas. ##C_V## is the coefficient of proportionality between internal energy on one hand and number of moles and temperature of the gas on the other hand.abdossamad2003 said:I was not convinced why internal energy should be written for heat capacity in constant volume. This process does not take place in constant volume, and if it is in constant volume, the change in internal energy must be zero.