Show that pressure of a fixed amount of a ideal gas is a state function`V=(nRT)/(p)`

Figure shows a process for a given amount of an ideal gas. If volume in state 1 is V_(1) & in state 2 is V_(2) , then

Figure shows a process for a given amount of an ideal gas. If volume in state 1 is V_(1) & in state 2 is V_(2) , then

Establish ideal gas equations (PV=nRT).

Which of the following is a correct plot of the volume of fixed amount of ideal gas as a function of temperature (at constant pressure)

Which of the following is a correct plot of the volume of fixed amount of ideal gas as a function of temperature (at constant pressure)

During an adiabatic process , the pressure p of a fixed mass of an ideal gas change by Deltap and its volume V change by DeltaV . If gamma=C_(p)//C_(v) then DeltaV//V is given by