Enthalpy and specific heats are key concepts in thermodynamics. They help us understand how energy moves in systems and how materials respond to temperature changes. This knowledge is crucial for analyzing heat transfer and energy transformations.
The first law of thermodynamics deals with energy conservation. Enthalpy and specific heats are tools that let us quantify energy changes in various processes, connecting nicely to the broader themes of the chapter.
Enthalpy and Specific Heats
Definition and Calculation of Enthalpy
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Enthalpy represents the total heat content of a system
Defined as the sum of the internal energy and the product of pressure and volume (H=U+pV)
Enthalpy is a state function, meaning its value depends only on the current state of the system, not the path taken to reach that state
Changes in enthalpy can be calculated using the specific heat capacity of a substance
Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree (units: J/kg·K)
The change in enthalpy (ΔH) is equal to the mass (m) times the specific heat capacity (c) times the change in temperature (ΔT): ΔH=mcΔT
Constant Pressure and Constant Volume Specific Heats
The specific heat capacity of a substance can vary depending on the conditions under which heat is added
Constant pressure specific heat (cp) is the amount of heat required to raise the temperature of a unit mass of a substance by one degree at constant pressure
Constant volume specific heat (cv) is the amount of heat required to raise the temperature of a unit mass of a substance by one degree at constant volume
For an ideal gas, the constant pressure specific heat is always greater than the constant volume specific heat
This is because at constant pressure, some of the added heat goes into doing work to expand the gas, while at constant volume, all of the added heat goes into increasing the internal energy (and thus temperature) of the gas
The relationship between cp and cv for an ideal gas is given by cp−cv=R, where R is the specific gas constant
Heat Transfer
Sensible Heat
Sensible heat refers to the heat that causes a change in temperature without a change in phase
When sensible heat is added or removed from a substance, its temperature changes, but it remains in the same phase (solid, liquid, or gas)
The amount of sensible heat transferred can be calculated using the specific heat capacity and the change in temperature (Q=mcΔT)
Examples of sensible heat transfer include:
Heating water in a pot on a stove (temperature increases, but water remains liquid)
Cooling a metal object by immersing it in cold water (temperature decreases, but metal remains solid)
Latent Heat
Latent heat is the heat absorbed or released by a substance during a phase change without a change in temperature
When a substance undergoes a phase change (melting, vaporization, freezing, or condensation), it absorbs or releases heat while maintaining a constant temperature
The amount of latent heat transferred depends on the mass of the substance and the specific latent heat for the phase change (fusion or vaporization)
Examples of latent heat transfer include:
Melting ice to form liquid water (heat is absorbed, but temperature remains at 0°C until all ice has melted)
Boiling water to form steam (heat is absorbed, but temperature remains at 100°C until all water has vaporized)
Thermodynamic Properties
Heat Capacity Ratio
The heat capacity ratio (γ) is the ratio of the constant pressure specific heat to the constant volume specific heat: γ=cp/cv
For an ideal gas, the heat capacity ratio is a constant that depends only on the number of degrees of freedom of the gas molecules
Monatomic gases (e.g., helium) have a heat capacity ratio of 5/3, diatomic gases (e.g., nitrogen) have a heat capacity ratio of 7/5, and polyatomic gases have lower values
The heat capacity ratio is an important parameter in many thermodynamic processes
It appears in the equation for the speed of sound in a gas: c=γRspecificT, where Rspecific is the specific gas constant and T is the absolute temperature
It also determines the relationship between pressure and volume during an adiabatic process (one with no heat transfer): pVγ=constant