Q.What will be the minimum pressure required to compress 500 dm3 of air at 1 bar to 200 dm3 at 30°C?
Concept understanding — Boyle's Law
You are sitting on a bicycle pump. The handle is up, the cylinder is full of air. Now push the handle down. The air inside gets squashed into a smaller space — its volume decreases. At the same time, you feel the resistance building: the air is pushing back harder. That is pressure increasing.
That is the raw physical feeling of Boyle's Law. Squeeze a gas, it fights back more. Let it expand, it relaxes.
Now the precise idea: if you take a fixed amount of gas (no air leaking in or out) and keep its temperature absolutely constant, then the volume it occupies and the pressure it exerts are inversely proportional. Double the pressure, the volume halves. Triple the pressure, the volume shrinks to one-third. Halve the pressure, the volume doubles.
Mathematically, this is written as:
P∝V1(at constant T and fixed mass)
Or, more usefully, as a product that stays constant:
PV=k
where k is some constant number for that particular sample of gas at that temperature.
P1V1=P2V2
This is the working form. If you know three of the four values (initial pressure, initial volume, final pressure, final volume), you can find the fourth.
Why does this happen? Imagine the gas as billions of tiny balls (molecules) zipping around in a box. Pressure comes from them banging into the walls. If you shrink the box, each molecule has less distance to travel between walls, so it hits the walls more often. More collisions per second means higher pressure. The molecules themselves haven't changed speed (temperature is constant), but they are now crowded into a smaller space, so the wall gets hit more frequently.
A very common mistake is to think pressure and volume are directly proportional — that increasing one increases the other. That is wrong for a fixed mass at constant temperature. They move in opposite directions. When one goes up, the other goes down.
A graph of pressure against volume is a curve that swoops downward — a rectangular hyperbola. A graph of pressure against 1/V is a straight line through the origin. That straight line is the signature of a perfect inverse proportion.
Boyle's Law: For a fixed mass of gas at constant temperature, the volume is inversely proportional to the pressure.
Boyle's law is one of the earliest gas laws taught in the NCERT/CBSE Class 11 Chemistry chapter on states of matter, and "Boyle's law: definition, formula & real-world examples" is a very frequently searched query for this topic. It's also a building block for ideal gas equation questions that appear consistently in JEE Main and NEET important-question lists.
Isothermal compression at 30°C — apply Boyle's law.
p2=2.5 bar
Step 1 – Identify the process
Temperature is fixed at 30°C throughout, so Boyle's law applies:
p1V1=p2V2
Step 2 – Data
p1=1 bar,V1=500 dm3,V2=200 dm3
Step 3 – Solve
p2=V2p1V1=200 dm3(1 bar)(500 dm3)=2.5 bar
p2=2.5 bar — this is the minimum pressure needed to compress the air into the smaller volume.
Apply Boyle's Law (p1V1=p2V2) since T is constant (30°C given only to confirm isothermal condition, not used numerically).
- Trying to use the 30°C value in a calculation — it's only there to establish that T is constant; Boyle's law needs no temperature substitution.
- Inverting the ratio (V2/V1 instead of V1/V2) when solving for p2.
- KEAM 2021Set eng-2021-P1-A14 marksMCQQ.A cycle tube will burst if the volume of air inside exceeds 1L at the room temperature. If at 1 bar pressure the air occupies 500 mL, then up to what pressure can the tube be expanded at the same temperature? (A) 2 bar (B) 1.5 bar (C) 0.5 bar (D) 0.002 bar (E) 1.2 bar
›Reveal solutionSolution
The tube reaches its 1 L bursting volume when the pressure drops to 0.5 bar.
Concept and Intuition
At constant temperature, pressure and volume are inversely related (Boyle's law). As the tube expands, its volume rises and the pressure of the enclosed air falls.
Step-by-Step Solution
- P1V1=P2V2 with P1=1 bar, V1=500 mL, V2=1000 mL.
- P2=10001×500=0.5 bar.
Common Mistakes
- Multiplying instead of applying the inverse relation and getting 2 bar.
✓Final answerThe correct option is (C) — 0.5 bar.
ANSWER: C
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