Physics4B vlgomez: 2nd Law of Thermodynamics and Heat Engines

Here we have the Thermoelectric Cooler experiment.

one of the plates was placed in the cold water and the other was placed in the hot water which caused it spin, when we reversed the position of the plate the propeller still moved but in the opposite direction. The work put into the propellor was caused by the big change in temperature.

Then a battery was added, which pumped heat into it. The system was now acting like a refrigerator.

Throughout most of the class today we derived various formulas using the ideal gas law and other known or given concepts. Here we derived the molar heat capacity at constant temperature.

This is where we began our next assignment, adiabatic changes and the P-V diagram. In this picture we show our work for part a, which asked:

For an ideal gas described by PV = nRT, use the fact that for small changes in pressure and volume Δ(PV) ≈ P ΔV + V ΔP and the relationship CP − CV = R to show that:

ndeltaT ≈ (P ΔV + V ΔP )/R = (P ΔV + V ΔP)/CP − CV

here we did parts b through e and proved that

γ = (C_P /C_V) = 5/3. which gave us our final result.

Here we did part f which says:

Use the result in part e. in conjunction with the ideal gas law to show that T_fV_f^γ–1 = T_iV_i^γ–

This is our next assignment work in adiabatic and isothermal expansions. This is where we consider the work associated with both adiabatic and isothermal expansions. Here we show our work for part a which says:

The result you just obtained previously can be written PV^γ = P_iV_i^γ or P = (V^−γ)P_iV_i^γ for any point in an adiabatic expansion. Use this to show that this adiabatic P − V relationship in conjunction with the equation for work, W = ∫PdV yields an adiabatic work equation of

Adiabatic work = [(PiVi^γ)( Vf^1-γ-Vi^1-γ)]/1-γ

part b:

Calculate the work done when one mole of 300 K gas expands adiabatically from an initial pressure of 8.31 × 10² N/m² and volume of 3.00 m³ to a final pressure of 3.02 × 10² N/m², a volume of 5.51 m³

This our sample Carnot cycle:

Here is a specific example of a Carnot cycle involving 1.00 moles of an ideal monatomic gas for which γ = 5/3. It has four “legs.” You will be using this sample cycle data in Activity 3.15.1 to make a series of specific calculations that should help you understand the relationship between the heat energy transfers and the temperatures of the reservoirs for a Carnot engine.

Our next activity is the analysis of the Carnot cycle. Here we calculated internal energy using the heat transfer (Q) and work.