4-1 Work and Heat
When two objects have different temperatures and were placed together, (Generally we say one is hot, the other is cold) they will reach the same temperature. During the processes to reach the final temperature, people may think there exists a substance or a form of matter termed caloric ( now we call that is heat ) in every body(which is wrong), and this substance transferred from hot to cold object. Though we know that heat is not a substance and heat is the something to have two objects to reach thermal equilibrium.
Definition of Heat: Heat is transferred between a system and its surroundings by virtue of a temperature difference only.
Adiabatic wall : no heat can transfer through this wall, heat insulator.
Adiabatic process: During adiabatic expansion and adiabatic compression, no heat will transfer between system and its surrounding.
Diathermic wall : heat can transfer through this wall completely, heat conductor.
Figure 4-1 a), it is adiabatic work, ( from right to left is adiabatic compression, while from left to right is adiabatic expansion) since the system is surrounded by adiabatic wall, note the temperature of system is irrelevant to its of the surroundings.
b), the system is heated up by its surroundings and heat is transfered into the system, but no work is done, since dV = 0.
c), Work and heat are done or transferred between system and its surroundings, this is the general case.
Work and heat have the same unit, so, during a state changed, does it perform a work or just the heat transferred. The answer of this question is " Find the system and its surroundings". Figure 4-2: can clearly specify this answer.
Weight (as a surroundings of resistance) do work to the Resistance system. The resistance ( as a system and water as surroundings) transferred heat to the water surroundings.
4-2 Adiabatic Work
Adiabatic System: A system is enclosed by an adiabatic boundary (or walls) and its temperature is independent of that of the surroundings, and this system may still be coupled to the surroundings so that work (not heat transferred) may be done. See Figure 4-3, and the work done between system and its surroundings is call adiabatic work.
Figure 4-4a is
Irreversible adiabatic process: Adiabatic free expansion, if the piston is moving faster than the velocity of liquid molecules contained inside the adiabatic walls, then the fluid will do no work on the piston.
Reversible adiabatic process: Move the piston slowly and it is a quasi-static processes, the fluid system is in quasi-equilibrium.
In figure 4-4b:
iaf path: ia is a reversible adiabatic process due to slowly moving pistons( can go both directions ia or ai), while the af is irreversible adiabatic and isothermal process. During af process (can only go one direction), the resisters dissipate electrical energy in conjunction with piston movements that keep the system at constant temperature.
ibf path: ib is an irreversible adiabatic and isothermal process, while the bf is a reversible process due to slowly moving pistons. During ib process, the resisters dissipate electrical energy in conjunction with piston movements that keep the system at constant temperature.
iedf path: ie is a reversible adiabatic process due to slowly moving pistons, and the ed is an irreversible process (free expansion), and df is an isochoric process (constant volume V and V') because the resisters dissipate electrical energy in conjunction with piston movements that keep the system at constant volume.
iebf path: ie is an irreversible adiabatic process (free expansion), and the eb is an isochoric process (constant volume) because the resisters dissipate electrical energy in conjunction with piston movements that keep the system at constant volume., and bf is a reversible process due to slowly moving pistons.
【Although accurate measurements of adiabatic work along different paths between the same two states have never been made, indirect experiments indicate that the adiabatic work is the same along all such paths.】 This implies that all the paths mentioned above have done the same amount of work, and the generalization of this result is known as the first law of thermodynamics:
→【If a system is caused to change from an initial state to a final state by adiabatic means only , the work done is the same for all adiabatic paths connecting the two states.】
The first law gives the following conclusion: the work done adiabatically is independent of path between initial and final states, and there exists a function of the coordinates of thermodynamic system. The adiabatic work done between initial and final states are equal to the difference of the function between initial and final states. The function is known as internal-energy function, U, which is
If the adiabatic work is done on the system, thus it is a positive work, the internal energy increases. From the discussion above, the adiabatic work done on the system is equal to increase of internal energy,→this simply expresses the principle of the conservation of energy.
4-3 Internal Energy Function
is the energy change of
the system, and U is a function of thermodynamic coordinates, also
it can specify the state of a system. General speaking, any function, which
is the function of thermodynamic coordinates, can be expressed as function
of any two thermodynamic coordinates because the third coordinate can be
linked through the equation of state. We can write dU as function
of θ and V,
if dU as a function of θ and P, we have
Note: 
.
4-4 Mathematical Formulation of the First Law of Thermodynamic
Nonadiabatic process: The work done during this process is not equal to the difference of internal energy between initial and final states(or simply say that the system is not surrounded by adiabatic wall, the temperature of system and its surroundings is related).
Question: What is the nonadiabatic process? For examples? (Figure 4-5)
Figure 4-5 a),the system is heated up by the heat source, through the diathermic wall.
b), Paramagnetic solid is surrounded by the liquid heliun, and they have temperature different, also the magnetic field is acting on the solid.
We know that the adiabatic work is equal to the change of internal energy,
thus energy of the system is conserved. If the work is nonadiabatic, then
it is not equal to 
. Due to
the concept of energy conservation, mathematically we can
rewrite the first law of thermodynamic as:
where Q is heat and W is the general work (not adiabatic work only), we are forced to conclude that energy has been transferred by means of heat other than the performance of work. Heat is transferred between system and its surroundings and this process has taken place only by virtue of the temperature difference between the system and its surroundings.
The first law contains three related ideas:
1. The existence of an internal-energy function, whose infinitesimal change is an exact differentials.
2. The principle of energy conservation.
3. The definition of heat as energy in transit by virtue of a temperature difference.
Re-define heat: 『When a system whose surroundings are at a different temperature and on which work may be done undergoes a process, the energy transferred by nonmechanical means, equal to the difference between the internal-energy change and the work done, is called HEAT.』
This means heat is a form of energy.
4-5 Concept of Heat
【Heat is internal energy in transit. It flows from one part of a system to another, or from one system to another, by virtue of only a temperature difference.】 The performance of work and the flow of heat are methods whereby the internal energy of a system is chanaged.
Since work W generally depend on the path and U is path independ function, so Q must be path-dependent. The first law is a path-independent function equal to two path dependent functions W and Q.
4-6 Differential Form of the First Law of Thermodynamics
For an infinitesimal quasi-static process, the first law can be express as
where only dU and 
can be
represented by the thermodynamic coordinates. For hydrostatic system, 
and the other systems can be check in Table 4-1. For example: the paramagnetic
gas system:
This is known as a Pfaffian differential form which is
inexact. This system has two independent thermodynamic coordinates, (θ,
P,V) and (θ,H,M).
To integrate 
, generally we
offen mutiply an intrgrating function to make it as an exact differential
( this is purely mathematical property. For simple system that undergoes
an infinitesimal quasi-static process, e.g. 
,
we can always find an integrating factor because there only two independent
thermodynamic coordinates. (the third one can be eliminated by the equation
of states). In general, a Pfaffian differential from containning three
differentials does not admit of an integrating factor. But for 
having three or more independent coordinates, it still can find an integrating
factor due to the second law of thermodynamics and the empirical temperature
θ. The intrgrating factor for 
with any number of independent variables is an arbitrary function of the
empirical temperature only and it is the same fumction for all systems.→this
gives the definition of absolute thermodynamic temperature.
4-7 Heat Capacity and Its Measurement
If a system undergoes a change of temperature from qi to qf during the transfer of Q units of heat, the average heat capacity of the system is defined as the ratio
Average heat capacity = 
The instantaneous value of heat capacity C is
→ C
= 
Specific heat: means the heat capacity per unit mass. Specific → Per Unit Mass.
Molar heat capacity c: The heat capacity per mole. Molar → Per Mole
Heat capacity can be positive, zero, negative or infinite (phase transition), depending on the process the system undergoes during the heat transfer.
Heat capacity at constant pressure: 
;
a function of P and θ.
Heat capacity at constant volume:
;
a function of V and θ.
The measurement of the heat capacity of solid is very important, because the numerical values of heat capacity provide one of the most direct means of verifying the calculations of theoretical physicists and of deciding on the validity of the assumptions constituting some of the modern theories.
測量熱容量現今多採用 electrical method, 如下圖
將樣品置於真空中並用導熱非常差的物質將其圍繞以避免熱的散失。利用熱電偶或電阻溫度計來測系統的溫度。c 為莫耳熱容量，Dq和Dt的測量如下圖:
Dq為溫度差，Dt為加熱時間。AB段溫度計與樣品接觸但加熱電源並為未啟動。BD段加熱電源啟動，DEAB段加熱電源關閉。F和G圍外插得到的。 4-8: 18世紀用水作為量取熱容量的方法。純水由升14.5℃到15.5℃所需之熱為一卡。 1cal = 4.1860 J
4-9 Equation for a Hydrostatic System
Cp、Cv的實驗值對理論的驗證十分重要。代入第一定律
上式對靜流體而言是一般式。 a) 若V是常數→dV=0，則
U可以用理論模型計算，Cv可以由實驗求出。兩相驗證則可以知理論的假設是否正確。 b) 若P是常數→dP=0，則
實驗上可以測量則可以推算
驗證理論。
4-10 熱庫
在準靜過程中系統與外界的溫差是非常小，且溫度的變化也是非常慢，一般假設系統的溫度是均勻的。這樣情況下熱的傳遞也是非常慢，如此熱的傳遞可以用熱力學坐標進行簡單的運算。要如何有慢且均勻的熱傳遞呢?熱庫是一方法。
Heat Reservior: (熱庫)一物體質量很大，可以吸收或放出無限量的熱量而本身溫度不會改變，且其他熱力學坐標亦不會改變。(或說有改變但很小而無法測知)
一個準靜過程，可以視為與一系列之不同溫度(其溫差很小)的熱庫相接觸，而所考慮之系統之溫度由θi變化到θf，則熱流量可以被計算。例如等壓準靜過程，
若是等壓準靜過程，則
對於其它系統的準靜過程，也是有類似的考慮與計算方法。