Q.42 A cylinder contains 50 πΏ of an ideal gas at a pressure of 50 ππ‘π. Assuming that
the temperature remains unchanged, the volume of the gas at 1 ππ‘π
is __________ πΏ (rounded off to the nearest integer)
Answer
The volume of the gas at 1 atm is 2500 L.
Problem Analysis
This question tests Boyle’s law for an ideal gas under isothermal conditions (constant temperature). Boyle’s law states that pressure (P) and volume (V) are inversely proportional: PβVβ = PβVβ.
Here, initial conditions are Pβ = 50 atm and Vβ = 50 L; final pressure is Pβ = 1 atm.
Step-by-Step Solution
- Rearrange Boyle’s law to solve for
Vβ: Vβ = (PβVβ)/Pβ - Substitute values: Vβ = (50 Γ 50)/1 = 2500 L
- The result is already an integer, so no rounding is needed.
Common Mistakes
- Forgetting inverse proportionality (using
Vβ = Vβ/Pβ) - Applying Charles’s law (volume-temperature relation) instead
- Ignoring temperature constancy which confirms Boyle’s law applies exclusively
Introduction
In cylinder ideal gas 50 L 50 atm 1 atm volume problems, Boyle’s law governs isothermal expansion for CSIR NET aspirants. A cylinder holds 50 L ideal gas at 50 atm; find volume at 1 atm (temperature constant). Answer: 2500 L.
Boyle’s Law Explained
Boyle’s law: PV = constant at fixed T, or PβVβ = PβVβ. Pressure drops 50-fold (50 atm to 1 atm), so volume rises 50-fold. Graph: hyperbolic P-V curve.
Detailed Calculation
- Given:
Pβ = 50 atm,Vβ = 50 L,Pβ = 1 atm - Vβ = (50 Γ 50)/1 = 2500 L
- Units consistent (L, atm); ideal gas assumes no deviations
CSIR NET Applications
Such cylinder ideal gas questions test gas laws basics. Similar: 20 cmΒ³ at 1 atm to 50 cmΒ³ yields 0.4 atm. Practice verifies inverse relation.
Real-World Examples
- Syringe compression: smaller volume, higher pressure
- Scuba tanks: expand gas volume at surface
- Always isothermal for Boyle’s law application
