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Thermodynamics Lab

Build PV diagrams by exploring different thermodynamic processes. Compare isothermal, adiabatic, isobaric, and isochoric paths. Calculate work done, understand the Carnot cycle, and discover the limits of heat engine efficiency.

Guided Experiment: Comparing Thermodynamic Processes

For the same initial state and final volume, which process — isothermal or adiabatic — produces more work? How do you expect the final temperatures to differ?

Write your hypothesis in the Lab Report panel, then click Next.

Gas molecules — particle speed reflects temperature

Controls

Initial Pressure2.00 atm
Initial Volume10.00 L
Initial Temperature300.00 K
Moles1.00 mol
Final Volume20.00 L

Results

Isothermal Process
W=nRTln⁡(V2/V1)W = nRT \ln(V_2/V_1)
Initial State
P: 2.000 atm
V: 10.00 L
T: 300.0 K
Final State
P: 1.231 atm
V: 20.00 L
T: 300.0 K
Work Done (W)
17.0639 L·atm
(1729.00 J)
Expansion (gas does work)

PV Diagram — Isothermal (Hyperbola)

Shaded region represents work done (area under curve)

Data Table

(0 rows)
#TrialProcessP initial(atm)V initial(L)T initial(K)P final(atm)V final(L)T final(K)Work(L·atm)
0 / 500
0 / 500
0 / 500

Reference Guide

Thermodynamic Processes

Four fundamental processes describe how gases change state:

  • Isothermal — constant temperature. Heat flows in or out to keep T fixed. PV = nRT stays constant.
  • Adiabatic — no heat exchange. Temperature changes instead. PVγ = const.
  • Isobaric — constant pressure. Volume changes linearly with temperature.
  • Isochoric — constant volume. No work is done (W = 0). Pressure changes with temperature.

Work in PV Diagrams

Work done by the gas equals the area under the PV curve.

Wiso=nRTln⁡ ⁣(V2V1)W_{\text{iso}} = nRT \ln\!\left(\frac{V_2}{V_1}\right)
Wadiab=P1V1−P2V2γ−1W_{\text{adiab}} = \frac{P_1 V_1 - P_2 V_2}{\gamma - 1}

Expansion (V₂ > V₁) gives positive work — the gas pushes the piston out. Compression is negative work.

First Law of Thermodynamics

Energy is conserved in any thermodynamic process.

ΔU=Q−W\Delta U = Q - W

Where ΔU is the change in internal energy, Q is heat added to the gas, and W is work done by the gas. For an isothermal process, ΔU = 0 so Q = W. For adiabatic, Q = 0 so ΔU = −W.

Carnot Cycle

The Carnot cycle sets the upper limit on heat engine efficiency using two reservoirs at temperatures Thot and Tcold.

η=1−TcoldThot\eta = 1 - \frac{T_{\text{cold}}}{T_{\text{hot}}}

No real engine can exceed Carnot efficiency. A larger temperature difference gives a higher maximum efficiency. At Tcold = 0 K the efficiency would be 1 (100%), but absolute zero is unattainable.