An ideal gas undergoes a process TV-x  = constant. Bulk modulus for that process is (P= pressure)

Given relation is Tv-x=constantfrom ideal gas equation PV=nRT⇒T=PVnR substitute in above equationPVnRV-x=constan⁡tPV-x+1= Constant differentiate(-x+1)V-x⋅dV⋅P+V-x+1⋅dP=0−dP.VdV=(-x+1)P Bulkmodulus =−dP.VdV=(1-x)P.