Thermodynamics: Heat, Work, and Energy Transfer
Heat, Work, and the First Law of Thermodynamics
Summary
The transfer of thermal energy is a form of energy transfer occurring as a result of a temperature difference. Energy inside a substance is a function of its state and usually increases with increasing temperature.
The calorie is the amount of heat required to raise the temperature of 1 g of water from 14.5 °C to 15.5 °C.
The mechanical equivalent of heat is 4186 J/cal.
The heat capacity, C, of any substance is defined as the amount of thermal energy required to raise the temperature of the substance by one degree Celsius. The thermal energy required to change the temperature of a substance by ΔT is:
Q = mcΔT
where m is the mass of the substance and c is its specific heat.
The thermal energy required to change the phase of a pure substance of mass m is:
Q = mL
The parameter L is called the latent heat of the substance and depends on the nature of the phase shift and the properties of the substance.
The work done by a gas as its volume changes by ΔV from an initial value Vi to a final value Vf is:
W = ∫ViVf P dV
where P is the pressure, which may vary during the process. To evaluate W, we must specify the nature of the process; that is, P and V must be known during each stage. Since the work done depends on the initial, final, and intermediate states, it depends on the path between the initial and final states.
The first law of thermodynamics states that when a system undergoes a change from one state to another, the change in internal energy is:
ΔU = Q – W
where Q is the heat transferred to (or from) the system and W is the work done by (or on) the system. Although both Q and W depend on the path from the initial to the final state, the quantity ΔU is independent of the path.
In a cyclical process (one that originates and terminates in the same state), ΔU = 0, and therefore, Q = W. This means that the thermal energy transferred to the system equals the work done during the cycle.
An adiabatic process is one in which no heat is transferred between the system and its surroundings (Q = 0). In this case, the first law yields ΔU = –W. That is, the internal energy changes as a result of work being done by (or on) the system.
In an adiabatic free expansion of a gas, Q = 0 and W = 0, so ΔU = 0. That is, the internal energy of the gas does not change in this process.
An isovolumetric process is one that occurs at constant volume. No expansion work is done in such a process.
An isobaric process is one that occurs at constant pressure. The work done in such a process is PΔV.
An isothermal process is one that occurs at constant temperature. The work done by an ideal gas during a reversible isothermal process is:
W = nRT ln (Vf / Vi)
Heat can be transferred by conduction, convection, and radiation.
Conduction can be viewed as an exchange of kinetic energy between molecules or electrons colliding. The rate at which heat flows by conduction through a slab of area A is:
H = –kA (dT / dx)
where k is the thermal conductivity and dT / dx is the temperature gradient.
In convection, the heated substance moves from one place to another.
Radiation: All bodies radiate and absorb energy in the form of electromagnetic waves. A body that is warmer than its surroundings radiates more energy than it absorbs, whereas a body that is cooler than its surroundings absorbs more energy than it radiates.
The net rate of energy gained or lost each second by an object as a result of radiation is:
Pnet = σAe(T4 – T04)