P1V1/TI = P2V2/T2 and PV=nRT what is the difference between them ?

There is no actual difference between them, one is just an application of the other.

The is defined as ##PV = nRT##; now, for a particular ideal gas under particular conditions, this equation can be used to determine the change in either gas (moles), or system (temperature, volume, pressure) paramaters.

In this particular case, the number of moles is held constant, while the other paramaters change. If the number of moles is held constant for an ideal gas for two states, we can derive

##n = (P_1V_1)/(RT_1) ## for state 1 and ##n = (P_2V_2)/(RT_2) ## for state 2. Given the fact that ##R## is constant as well, this becomes

##(P_1V_1)/(T_1) = (P_2V_2)/(T_2)##, also known as the .

Essentially, this equation illustrates how pressure (##P##), volume (##V##), and temperature (##T##) interact with eachother when we have a change in the system's paramaters.