A kilogram of air is compressed from 1 m3 to 0.5 m3. Which statement is true?

Question

A kilogram of air is compressed from 1 m3 to 0.5 m3. Which statement is true??  
A. The density is doubled.  
B. The density is halved.  
C. The mass is doubled.  
D. The mass is halved.

Accepted Answer

Correct Answer: (A)The density is doubled.. 
Rationale: Compressing a kilogram of air from 1 m³ to 0.5 m³ doubles its density while leaving mass unchanged.Density, defined as mass per unit volume (ρ = m/V), responds inversely to volume when mass remains constant, halving the volume concentrates the same kilogram of air into half the space, precisely doubling the mass-to-volume ratio from 1 kg/m³ to 2 kg/m³.A) The density is doubled.Density equals mass divided by volume. Initially, density = 1 kg / 1 m³ = 1 kg/m³. After compression, density = 1 kg / 0.5 m³ = 2 kg/m³. The density precisely doubles because volume is halved while mass remains unchanged at one kilogram. This inverse relationship between density and volume under constant mass conditions makes this statement correct.B) The density is halved.Halving density would require either halving the mass or doubling the volume, neither occurs during compression. Since volume decreases rather than increases, density must increase rather than decrease. This option contradicts the fundamental definition of density and the physical process described.C) The mass is doubled.Mass represents the quantity of matter present and remains conserved during mechanical compression processes that don't involve nuclear reactions or matter addition/removal. The problem explicitly states "a kilogram of air" undergoes compression, confirming mass remains fixed at 1 kg throughout the process. No mechanism exists in simple compression to create additional matter.D) The mass is halved.Mass conservation is a fundamental principle in classical physics. Compression rearranges existing molecules into a smaller volume but doesn't eliminate matter. The air sample retains all its original molecules, only their spatial distribution changes. Halving mass would require physically removing half the air, which the problem doesn't describe.ConclusionDensity varies inversely with volume when mass remains constant. Compressing a fixed mass of gas to half its original volume necessarily doubles its density while leaving mass unchanged. This principle underlies gas behavior in engines, atmospheric science, and respiratory physiology, where volume constraints directly impact material density without altering total mass content.

A kilogram of air is compressed from 1 m3 to 0.5 m3. Which statement is true?

A
The density is doubled.

B
The density is halved.

C
The mass is doubled.

D
The mass is halved.

Compressing a kilogram of air from 1 m³ to 0.5 m³ doubles its density while leaving mass unchanged.

Topic Flashcards

Mini Quiz

Related Questions

A kilogram of air is compressed from 1 m3 to 0.5 m3. Which statement is true?

A The density is doubled. B The density is halved. C The mass is doubled. D The mass is halved.

Compressing a kilogram of air from 1 m³ to 0.5 m³ doubles its density while leaving mass unchanged.

Topic Flashcards

Mini Quiz

Related Questions

A
The density is doubled.

B
The density is halved.

C
The mass is doubled.

D
The mass is halved.