Gas Laws and Atmospheric Variables Questions and Answers

Answer: A

Written per unit mass the equation of state is \( p = \rho R T \), with \( R \) the specific gas constant for the gas concerned and \( T \) the absolute temperature. It is the starting point for essentially every calculation in atmospheric thermodynamics, and rearranging it to obtain density from pressure and temperature is the single most frequently performed operation in the subject. The other forms listed are dimensionally inconsistent and would not reproduce the observed behaviour of air under any conditions.

Answer: B

Dividing the universal gas constant of 8.314 joules per mole per kelvin by the mean molecular mass of dry air, 0.02897 kilograms per mole, gives 287 joules per kilogram per kelvin. Water vapour, being lighter, has the larger value of 461. The universal constant applies per mole rather than per kilogram, and the specific heat capacity is a related but distinct quantity that appears in the first law rather than in the equation of state. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Answer: C

Water has a molecular mass of 18 grams per mole against 29 for dry air, so its specific gas constant is correspondingly larger at 461 joules per kilogram per kelvin. The ratio of the two constants, about 0.622, appears throughout moist thermodynamics and is worth committing to memory. The latent heat is a quite different quantity that happens to be numerically memorable.

Answer: D

The constant epsilon equals 18.016 divided by 28.97, or about 0.622, and it converts between vapour pressure and mixing ratio in every moist thermodynamic formula. It is also the ratio of the dry air gas constant to the water vapour gas constant. The ratio of specific heats is conventionally denoted gamma, and the ratio of vapour pressure to total pressure is the mole fraction rather than a fixed constant. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Answer: A

Vapour pressure is the partial pressure of the water vapour component and is denoted \( e \), while the saturation value is the maximum sustainable over a plane water surface at that temperature. Dalton's law states that the total pressure is the sum of the partial pressures of the constituents. Relative humidity is the ratio of the two vapour pressures and dew point is a temperature, so both are derived quantities. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Answer: B

Dalton's law of partial pressures allows moist air to be treated as a mixture in which each component obeys the ideal gas law independently. It is what permits the vapour pressure to be handled separately from the dry air pressure. Boyle, Charles and Avogadro each described a different relationship among pressure, volume, temperature and quantity, and the ideal gas law combines all three into a single statement. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.

Answer: C

The mixing ratio is defined per unit mass of dry air, while specific humidity is defined per unit mass of moist air, so the two differ by a factor of one plus the mixing ratio. Since the mixing ratio rarely exceeds 0.04, the two are numerically close and the distinction is often ignored in practice. Absolute humidity is the mass of vapour per unit volume and is rarely used because it changes with pressure. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Answer: D

The relation \( w = \epsilon e/(p-e) \) follows directly from applying the ideal gas law to each component and taking the ratio of the masses. Because \( e \) is usually small compared with \( p \), the approximation \( w \approx \epsilon e/p \) is often used and is accurate to about one per cent in the lower troposphere. Deriving the exact form once makes the approximation easy to justify when it is needed. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Answer: A

Relative humidity expresses how close the air is to saturation and is conventionally given as a percentage. Because the saturation value depends strongly on temperature, relative humidity changes as air is heated or cooled even when no water is added or removed, which is why it is a poor measure of the actual moisture content. Mixing ratio and specific humidity are conserved under such changes and are preferred for that reason. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.

Answer: B

Warming raises the saturation vapour pressure while leaving the actual vapour pressure unchanged, so the ratio falls. This is why heated indoor air in winter feels dry despite containing the same amount of water as the cold air outside. The common phrase about warm air holding more water is misleading, since the vapour pressure depends on temperature rather than on any capacity of the air to contain it. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.