First Law Applied to the Atmosphere Questions and Answers

Answer: A

The first law is a statement of energy conservation: heat supplied to a system either raises its internal energy or is spent doing work on the surroundings. For a gas the work is the pressure times the change in volume. The second option states the second law, the third is a consequence of it, and the fourth is the equation of state, which is an independent relation. Applying the first law to a parcel of air moving vertically is what produces the adiabatic lapse rate and the whole framework of atmospheric thermodynamics.

Answer: B

As a parcel rises the surrounding pressure falls, so the parcel expands and does work on its surroundings, and with no heat supplied that work comes from its internal energy. The temperature therefore falls. Gravity acts on the parcel but the work against gravity appears as potential energy rather than as a loss of internal energy, which is a distinction worth keeping clear. The Coriolis force does no work at all because it acts perpendicular to the motion.

Answer: C

For an ideal gas the internal energy depends only on temperature, being the specific heat at constant volume multiplied by the absolute temperature. This is why the first law for a gas can be written entirely in terms of temperature and volume changes. Pressure, volume and density all appear in the equation of state but none of them determines the internal energy on its own. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Answer: D

At constant volume no work is done, so all the heat supplied raises the internal energy, and the specific heat is 718 joules per kilogram per kelvin for dry air. At constant pressure the gas must also do work of expansion, so more heat is needed for the same temperature rise, giving 1005. The difference of exactly 287 is the specific gas constant. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Answer: A

For an ideal gas \( c_p - c_v = R \), which follows from the definition of enthalpy together with the equation of state. With 1005 and 718 for dry air the difference is exactly 287. This identity is worth carrying because it lets any one of the three constants be recovered when memory fails, and it also explains physically why heating at constant pressure requires more energy. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Answer: B

Enthalpy combines the internal energy with the flow work, and its change at constant pressure equals the heat supplied. That is why the specific heat at constant pressure appears so often in atmospheric work, where processes are frequently isobaric or nearly so. For an ideal gas the enthalpy, like the internal energy, depends only on temperature. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Answer: C

Writing the law in terms of enthalpy gives \( dq = c_p dT - \alpha dp \), where alpha is the specific volume, and this is the form used throughout meteorology. It is convenient because atmospheric parcels change pressure as they move vertically. Setting the heat term to zero and substituting hydrostatic balance immediately gives the dry adiabatic lapse rate. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Answer: D

Adiabatic means no heat crosses the boundary of the parcel, though work may still be done and the temperature may change considerably. Vertical motion in the atmosphere is very nearly adiabatic because it is fast compared with radiative and conductive exchange. A reversible adiabatic process conserves entropy, which is why potential temperature is conserved along it. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Answer: A

Setting the heat term to zero and substituting hydrostatic balance gives a lapse rate of \( g/c_p \), which is 9.81 divided by 1005, or 9.8 kelvin per kilometre. It is very nearly constant because gravity and the specific heat both vary little. The environmental lapse rate is a property of the observed atmosphere rather than of a parcel and is quite different. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.

Answer: B

The rate \( g/c_p \) contains neither temperature nor pressure, which is why the dry adiabat is a straight line of essentially constant slope on a thermodynamic diagram. Humidity changes the specific heat very slightly, giving a rate of about 9.7 rather than 9.8 for very moist air, but the effect is negligible in practice. The constancy is what makes the dry adiabat so useful as a reference line. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.