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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+pVH = 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\Delta H) is equal to the mass (mm) times the specific heat capacity (cc) times the change in temperature (ΔT\Delta T): ΔH=mcΔT\Delta H = mc\Delta T

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 (cpc_p) 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 (cvc_v) 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 cpc_p and cvc_v for an ideal gas is given by cpcv=Rc_p - c_v = R, where RR 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=mcΔTQ = mc\Delta T)
  • 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\gamma) is the ratio of the constant pressure specific heat to the constant volume specific heat: γ=cp/cv\gamma = c_p / c_v
    • 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=γRspecificTc = \sqrt{\gamma R_specific T}, where RspecificR_specific is the specific gas constant and TT is the absolute temperature
    • It also determines the relationship between pressure and volume during an adiabatic process (one with no heat transfer): pVγ=constantpV^\gamma = constant


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AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
Glossary
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