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

given Tvx=constant; T is temeperature; V is volume;  from ideal gas equation T=PVnRsubstitute in given equationPVnRVx=cons⁡tan⁡tPVx+1=Constantdifferentiate(x+1)Vx⋅dV⋅P+Vx+1⋅dP=0(x+1)Vx⋅dV⋅P=-Vx+1⋅dP(x+1)P=-Vx+1dPVxdV−dP⋅VdV=(x+1)P    ; here left hand side of equation is bulk modulus=-dPdVV Bulk modulus =(x+1)P.