ME 101-Thermodynamics: Ideal Gas and Specific Heats

This set of vocabulary flashcards covers the fundamental gas laws, the ideal gas equation of state, specific heat properties, and thermodynamic relationships like internal energy and entropy for an ideal gas.

Ideal Gas

A gas that conforms to simple perfect gas laws, assuming negligible molecular volume, no intermolecular forces, constant random motion, and perfectly elastic collisions.

Boyle’s Law

States that if the temperature of a given quantity of gas is held constant, the volume of the gas varies inversely with the absolute pressure ($p_1 V_1 = p_2 V_2$).

Charles’ Law

States that if the pressure on a particular quantity of gas is held constant, the volume will vary directly as the absolute temperature ($\frac{V_1}{T_1} = \frac{V_2}{T_2}$).

Gay-Lussac’s Law

States that if the volume of a particular quantity of gas is held constant, the pressure will vary directly as the absolute temperature ($\frac{p_1}{T_1} = \frac{p_2}{T_2}$).

Combined Gas Law

A mathematical relationship combining Boyle’s, Charles’, and Gay-Lussac’s Laws, expressed as $\frac{p_1 V_1}{T_1} = \frac{p_2 V_2}{T_2}$, where $\frac{pV}{T} = \text{constant}$.

Avogadro’s Law

States that the volume $V$ of a sample of gas is directly proportional to the number of moles $n$ in the sample at constant temperature $T$ and pressure $P$ ($\frac{V_1}{n_1} = \frac{V_2}{n_2}$).

Universal Gas Constant ($R$)

The constant used in the equation of state for moles, equal to $8.3144\,J\,mol^{-1} \cdot K^{-1}$ or $1545\,Btu\,lbm \cdot mol^{-1} \cdot {}^\circ R^{-1}$.

Specific Gas Constant ($R_{specific}$)

Calculated by dividing the universal gas constant by the molar mass ($M$) of a specific substance; for air, it is approximately $287\,J\,kg^{-1} \cdot K^{-1}$ or $53.342\,lbf \cdot ft\,lbm^{-1} \cdot {}^\circ R^{-1}$.

Specific Heat ($c$)

The quantity of heat required to change the temperature of a unit mass through one degree ($c = \frac{dQ}{m\,dT}$).

Constant Volume Specific Heat ($c_V$)

The specific heat used when volume is constant, where the heat transferred equals the change in internal energy ($Q_V = \Delta U = m c_V (T_2 - T_1)$).

Constant Pressure Specific Heat ($c_p$)

The specific heat used when pressure is constant, where the heat transferred equals the change in enthalpy ($Q_p = \Delta H = m c_p (T_2 - T_1)$).

Ratio of Specific Heats ($k$)

The ratio of the specific heat at constant pressure to the specific heat at constant volume ($k = \frac{c_p}{c_V}$), which is always greater than 1.

Joule’s Law

States that the change of internal energy ($\Delta U$) of an ideal gas is a function of only the temperature change, regardless of whether volume remains constant ($\Delta U = m c_V (T_2 - T_1)$).

Enthalpy of an Ideal Gas ($\Delta H$)

The change in enthalpy, calculated as $\Delta H = m c_p (T_2 - T_1)$, which holds true whether the pressure remains constant or not.

Entropy ($S, s$)

A substance property that remains constant if no heat enters or leaves while the substance does work, defined differentially as $dS = \frac{dQ}{T}$ and for constant specific heat as $\Delta S = m c \ln\left(\frac{T_2}{T_1}\right)$.