First Law of Thermodynamics

What is the First Law of Thermodynamics?

dU = dQ + dW 

dU = change in internal energy

dQ = heat added to the system

dW = work done by the system

How is the internal energy of an ideal gas calculated?

dU=m.c_v.​ΔT

Where:

• m = Mass of gas (kg)

• c_v = Specific heat at constant volume (J/kgK).

• ΔT = Change in temperature (K).

What is the formula for work done by the system?

W=pΔV

• p = Pressure (Pa)

• ΔV = Volume change (mDefine adiabatic processes.)

Define adiabatic processes.

• Adiabatic Process: No heat exchange with surroundings (Q=0Q = 0Q=0).

• Temperature changes occur due to expansion (cooling) or compression (warming).

Define diabatic processes.

• Diabatic Process: Heat is exchanged with surroundings (Q≠0Q \neq 0Q=0).

• Common examples: Solar heating, radiative cooling, latent heat release.

What is potential temperature (θ)?

θ=T(p₀/p​​)^R/cp​

The temperature an air parcel would have if brought adiabatically to a reference pressure (1000 hPa)

Why is potential temperature (θ\thetaθ) useful?

It is conserved during adiabatic processes and helps determine atmospheric stability:

• Stable Atmosphere: θ increases with height.

• Unstable Atmosphere: θ decreases with height.

What happens to a rising air parcel in an adiabatic process?

• Expands as pressure decreases.

• Does work on surroundings, losing internal energy.

• Temperature decreases (adiabatic cooling).

What happens to a sinking air parcel in an adiabatic process?

• Compresses as pressure increases.

• Work is done on the parcel, gaining internal energy.

• Temperature increases (adiabatic warming).

How does latent heat affect diabatic processes?

• Latent Heat Release: During condensation, heat is released, warming the air.

• Latent Heat Absorption: During evaporation, heat is absorbed, cooling the air.
  This process drives convection and cloud formation.

Write the First Law for an adiabatic process.

dU = -dW

Since dQ = 0, internal energy changes is due to any work being on/by the system

Write the First Law for a diabatic process.

Q=c_p​ΔT−pΔV/m​

Heat transfer affects both temperature and work done.

Why does potential temperature remain constant during adiabatic processes?

No heat is added or removed, so θ reflects only the effect of pressure changes on temperature.

What is the dry adiabatic lapse rate?

9.8K/km

Compare adiabatic and diabatic cooling.

• Adiabatic Cooling:

  • Temperature decreases due to expansion (e.g., rising air).

  • Causes cloud formation as air parcels cool and reach saturation.

  • Drives convection and precipitation.

• Diabatic Cooling:

  • Temperature decreases due to heat loss (e.g., radiative cooling).

  • Leads to fog or frost formation near the surface.

  • Common during clear nights with radiative heat loss.