U is a function of temperature only. It does not depend on volume or pressure (although those will affect temperature, of course). dU is always = mC(v)dTAmith2006 said:In the above derivation, when volume is changing, how can they take dU = mC(v)dT?
Here m = mass of gas,r = gas constant,J = Mechanical equivalent of heat
An isobaric process is a type of thermodynamic process in which the pressure of a system remains constant while other variables, such as temperature or volume, change. This means that the system is experiencing a change in energy while being held at a constant pressure.
Del(H) represents the change in enthalpy of the system. Enthalpy is a measure of the total energy of a thermodynamic system, including both its internal energy and the amount of work required to change its volume at constant pressure.
mC(v)dT represents the change in internal energy of the system. It takes into account the mass of the system (m), the specific heat capacity at constant volume (C(v)), and the change in temperature (dT).
(P.dV)/J represents the work done by the system. Work is defined as the force applied to an object multiplied by the distance traveled in the direction of the force. In this equation, it takes into account the change in pressure (P) and the change in volume (dV).
The equation is derived from the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. In an isobaric process, the work done is equal to the change in pressure multiplied by the change in volume, and the heat added is equal to the change in enthalpy. Therefore, the equation for an isobaric process is del(H) = mC(v)dT + (P.dV)/J.