Adiabatic temperature changes result from which of the following conditions in the atmosphere?

A cylinder contains $0.0100$ mol of helium at $T = 27.0$°C. What accounts for the difference between your answers to parts (a) and (b)? In which case is more heat required? What becomes of the additional heat?

(a) How much heat is needed to raise the temperature to $67.0$°C while keeping the volume constant? Draw a $pV$-diagram for this process.

(b) If instead the pressure of the helium is kept constant, how much heat is needed to raise the temperature from $27.0$°C to $67.0$°C? Draw a $pV$-diagram for this process.

A cylinder contains $0.0100$ mol of helium at $T = 27.0$°C. If instead the pressure of the helium is kept constant, how much heat is needed to raise the temperature from $27.0$°C to $67.0$°C? Draw a $pV$-diagram for this process.

A cylinder contains $0.0100$ mol of helium at $T=27.0$°C. How much heat is needed to raise the temperature to $67.0$°C while keeping the volume constant? Draw a $pV$-diagram for this process.

(II) A 1.00-mol sample of an ideal diatomic gas, originally at 1.00 atm and 20°C, expands adiabatically to 1.75 times its initial volume. What are the final pressure and temperature for the gas? (Assume no molecular vibration.)

How much heat energy is needed to increase the temperature of 5 mol of an ideal diatomic gas by from 273K to 300K if the a) pressure is held constant; b) the volume is held constant?

The temperature of $0.150$ mol of an ideal gas is held constant at $77.0$°C while its volume is reduced to $25.0\%$ of its initial volume. The initial pressure of the gas is $1.25$ atm. Does the gas exchange heat with its surroundings? If so, how much? Does the gas absorb or liberate heat?

A cylinder contains 0.100 mol of an ideal monatomic gas. Initially the gas is at $1.00\times {10}^5$ Pa and occupies a volume of $2.50\times {10}^{-3}$ m³. If the gas is allowed to expand to twice the initial volume, find the final temperature (in kelvins) and pressure of the gas if the expansion is (i) isothermal; (ii) isobaric; (iii) adiabatic.

On a warm summer day, a large mass of air (atmospheric pressure $1.01\times {10}^5$ Pa) is heated by the ground to $26.0$°C and then begins to rise through the cooler surrounding air. (This can be treated approximately as an adiabatic process; why?) Calculate the temperature of the air mass when it has risen to a level at which atmospheric pressure is only $0.850\times {10}^5$ Pa. Assume that air is an ideal gas, with $g=1.40$. (This rate of cooling for dry, rising air, corresponding to roughly $1$ C° per $100$ m of altitude, is called the dry adiabatic lapse rate.)