Key relationship
pV=nRT; Wisothermal=∫p dV=nRTln(V₂/V₁).
Physics · Class 11
Compress an ideal gas isothermally
Pressure rises as an isothermal gas is compressed. The work is the area under its inverse-volume pressure curve, giving a logarithm rather than simply multiplying one pressure by the volume change.
Open the interactive experiment →Compress an ideal gas isothermally
சமவெப்ப சுருக்கத்தில் அழுத்தம் அதிகரிக்கும். வாயு செய்த வேலை nRT ln(V₂/V₁); சுருக்கத்தில் அது எதிர்மறை.
Key notes, relationships and model limits
Remember
Pressure rises as an isothermal gas is compressed. The work is the area under its inverse-volume pressure curve, giving a logarithm rather than simply multiplying one pressure by the volume change.
Common trap
Using final pressure times volume change overestimates the compression work.
Model limits
Quasistatic isothermal compression or expansion of an ideal gas. Heat exchange maintains temperature. Work is positive for expansion and negative for compression.
What you will learn
Calculate compression work with the ideal-gas equation.
Try the experiment
Try both scenarios, change one control, and predict the result before checking the graph and readouts.
Think of it this way
Change one input while keeping the others fixed, as you would in a controlled experiment.
Worked example
The starting 10 L gas has p≈249.43 kPa; at 5 L it has p≈498.87 kPa. Work done on the gas is +1728.9 J and heat out is the same magnitude.
Why this matters
The model connects compress an ideal gas isothermally with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
Compress 1 mol at 300 K to half its volume. What work does the gas do?
- About +1729 J
- About −1729 J
- About −2494 J
Read the explanation
W=RTln0.5≈−1728.9 J.
Course connection: Class XI Chapter 12. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.