Two constant$-$volume gas thermometers are assembled, one with nitrogen and the other with hydrogen. Both contain enough gas so that $p_3=85\mathrm{.}0$kPa. $($a$)$ What is the difference between the pressures in the two thermometers if both bulbs are in boiling water? $($Hint: See the figure.$)($b$)$ Which gas is at higher pressure, nitrogen or hydrogen?

Indications of the constant$-$volume gas thermometer for a boiling point of water depending on pressure at the triple point of water for various gases