Key relationship
B=−V(dp/dV); Bisothermal=p; Badiabatic=γp. Finite p₂=p₁/(1−c)^n.
Physics · Class 11
Compare fast and slow gas compression
A gas compressed without cooling becomes hotter and resists more strongly than a gas allowed to remain isothermal. Consequently its adiabatic bulk modulus is γ times its isothermal value at the same starting pressure.
Open the interactive experiment →Compare fast and slow gas compression
வெப்பம் வெளியேறாத சுருக்கத்தில் வாயு சூடாகி அதிக எதிர்ப்பு தரும். வெப்பமாற்றமற்ற பருமக் குணகம் γp ஆகும்.
Key notes, relationships and model limits
Remember
A gas compressed without cooling becomes hotter and resists more strongly than a gas allowed to remain isothermal. Consequently its adiabatic bulk modulus is γ times its isothermal value at the same starting pressure.
Common trap
The bulk modulus of a gas depends on the process as well as the current state.
Model limits
Ideal gas with constant γ. Slow temperature-controlled compression is isothermal; reversible insulated compression is adiabatic. Moduli are differential values at the initial state.
What you will learn
Distinguish differential moduli from finite compression laws.
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
A 10% compression gives p₂,isothermal=100/0.9=111.11 kPa and p₂,adiabatic=100/0.9¹·⁴≈115.90 kPa.
Why this matters
The model connects compare fast and slow gas compression with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
At p=100 kPa and γ=1.4, what is adiabatic bulk modulus?
- 100 kPa
- 140 kPa
- 71.4 kPa
Read the explanation
Bad=γp=1.4×100 kPa.
Course connection: Class XI Chapter 11. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.