Thermal Physics Quiz: Air Temperature in a Cabin

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Study Notes

The first law states conservation of energy: the heat lost by a hotter gas equals the heat gained by a cooler gas, expressed as Q1 = Q2.
For an ideal gas, internal energy change (ΔE_int) is a result of absorbed heat (Q) and work done (W): ΔE_int = Q + W.
In an adiabatic process (no heat exchange), ΔE_int = dW, leading to the equation ΔE_int = -dW.

Internal energy change for ideal gases can be represented as ΔE_int = nC_VΔT, where n is the number of moles and C_V is the specific heat capacity at constant volume.
Ideal gas law relates pressure (P), volume (V), and temperature (T): PV = nRT.

Adiabatic Process: Insulated system where no heat enters or leaves (dQ = 0).
- Results in work done (W) changing internal energy (ΔE_int = dW).
Isothermal Process: Temperature remains constant (ΔE_int = 0).
- Heat exchange equals negative work done (Q = -W).
Constant Volume Process: No work is done (W = 0).
- All heat absorbed contributes to internal energy (ΔE_int = Q).
Cyclical Process: Returns to the initial state, leading to a net change in internal energy of zero (ΔE_int = 0). Relationship given by Q + W = 0.
Free Expansion: Expansion occurs without external pressure applied, leading to no work done and no heat exchange.

For any infinitesimal change, the differential form of the first law can be expressed as dE_int = dQ + dW.
In adiabatic processes, changes in pressure and volume can be modeled mathematically to show specific relationships between temperature and volume (T V^(γ - 1) = constant).

In cyclical processes, the net work done can be characterized by the paths taken and whether they are clockwise (work done on the system) or counterclockwise (work done by the system).

The processes and equations are crucial for understanding how energy is transferred and transformed within thermodynamic systems, particularly in systems involving ideal gases.

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