An ideal gas obeys VP²=constant. Initially temperature T and volume V; when volume increases to 2V, temperature becomes √x·T. Find x.
Physics · Mixed Chapter
JEE Main Practice

Question

An ideal gas obeys VP²=constant. Initially temperature T and volume V; when volume increases to 2V, temperature becomes √x·T. Find x.

G1 Physics · Accepted Answer

Step 1: VP²=C⇒P∝V⁻¹⁄². Step 2: For V₂=2V₁, P₂/P₁=1/√2. Step 3: Ideal-gas temperature T∝PV, so T₂/T₁=(P₂/P₁)(V₂/V₁)=(1/√2)×2=√2. Step 4: Thus √x=√2 ⇒x=2.