Describe the pressure–volume relationship indicated by the $300\ \mathrm{K}$ measurements.

For the measurements at $V=2.00\ \mathrm{L}$ calculate $PV/T$ at each temperature. Give an appropriate unit.

A fixed amount of gas changes from state 1 $(P_1,V_1,T_1)$ to state 2 $(P_2,V_2,T_2)$ Using the empirical pressure–temperature law at constant volume and Boyle’s law at constant temperature, derive a relation between these two states. Temperatures are in kelvin.

A controller is expected to switch when the gas reaches $750\ \mathrm{K}$ Use state $X$ and both calibration results from part (b) to estimate the temperature at $X$ and decide whether the controller’s reported temperature is consistent with the measurements. Show your working.