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## 物理代写|热力学代写thermodynamics代考|INTERNAI ENERGY AND ADIARATIC WORK

Work done by a force is defined as the product of the force and the displacement in the direction of the force. In thermodynamics, we are mostly concerned with work associated with the volume changes of a system. If ” $p$ ” denotes the pressure that the system exerts on its boundary and ” $d V$ ” is the volume change, then ” $p d V$ ” is the work done by the system when the system increases its volume by ” $d V$ “.

The difference in the pressure across the boundary of the system must be infinitesimally small giving rise to a fully resisted motion of the boundary in order to define work done by the system. The rate of expansion is thus sufficiently slow to permit both the system and the environment that it interacts with to be in equilibrium at all times.

The work done by the system between two equilibrium states is given by the integral
$$W=\int_{V_1}^{V_2} p d V$$
The above integral is a path integral and the path $p(V)$ must be specified in order to evaluate the integral. Also between the same two states, the work done is different for different paths; we therefore say that the work is a path-dependent quantity.

There are different kinds of work other than ” $p d V$ ” work and also the work may not necessarily be associated with the change in the configuration of the system (like the volume). For example, the work input to a system, such as by a paddle wheel as mechanical work, does not involve a change in the configuration of the system. This is generally defined as dissipative work where the mechanical work input to the system is converted via viscous dissipation to heat, hence increasing the internal energy of the system.

When the system is insulated and hence there is no heat exchange with the environment, the work done either by or on the system is referred to as adiabatic work. Experiments indicate that adiabatic work done by (or on) the system between two equilibrium states is the same for different adiabatic processes. From Eq. 3.1, we can write
$$\Delta U=-W_{a d}$$
where $W_{a d}$ is the adiabatic work done by the system. Since $W_{a d}$ is path-independent, the internal energy change between two states is also path-independent.

We can therefore define a state function ” $U$ ” such that the change in the state function can be determined by measuring the adiabatic work input to the system.

Internal energy can be understood at a more fundamental level based on the atomistic view of matter. However, as per the first law, the internal energy difference between two equilibrium states can be defined via a macroscopic measurement of the adiabatic work input to the system.

## 物理代写|热力学代写thermodynamics代考|HEAT CAPACITY OF A SYSTEM

In the absence of phase changes, the heat transfer to a system results in a temperature rise. The heat capacity ” $C$ ” of a system is defined as
$$C=\lim {\Delta T \rightarrow 0} \frac{Q}{\Delta T}=\frac{\delta Q}{d T}$$ Since ” $Q$ ” is a path-dependent quantity, $\delta Q$ in Eq. $3.5$ is not a total differential. Equation $3.5$ should not be interpreted as the derivative of ” $Q$ ” with respect to ” $T$ “. Since $\delta Q$ is path-dependent, we define the heat capacities for different heat transfer processes. For a constant volume process, we write the heat capacity at constant volume as $$C_v=\lim {\Delta T \rightarrow 0} \frac{\delta Q_v}{\Delta T}$$
where $\delta Q_v$ is the heat transfer under constant volume conditions. Similarly, for a constant pressure process, we define heat capacity at constant pressure as
$$C_p=\lim _{\Delta T \rightarrow 0} \frac{\delta Q_p}{\Delta T}$$

# 热力学代写

## 物理代写|热力学代写thermodynamics代考|INTERNAI ENERGY AND ADIARATIC WORK

$$W=\int_{V_1}^{V_2} p d V$$

$$\Delta U=-W_{a d}$$

## 物理代写|热力学代写thermodynamics代考|HEAT CAPACITY OF A SYSTEM

$$C=\lim \Delta T \rightarrow 0 \frac{Q}{\Delta T}=\frac{\delta Q}{d T}$$

$$C_v=\lim \Delta T \rightarrow 0 \frac{\delta Q_v}{\Delta T}$$

$$C_p=\lim _{\Delta T \rightarrow 0} \frac{\delta Q_p}{\Delta T}$$

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