請問，一個8L(水容量)的鋼瓶裏有30000psi空氣，連接一個沒有空氣的4.3L(水容量)鋼瓶 問: 1)連接後兩個瓶的壓力? 數式? 2)若4.3L的鋼瓶本來已有10000psi空氣，連接後的壓力?數式? 感謝解答?

(1) Using Boyle's Law,
30000 x 8 = P x (8 + 4.3)
where P is the final pressure after the two steel vessels are connected.
Hence, P = 30000 x 8/(8 + 4.3) psi = 19,512 psi

(2) Using the Ideal Gas Equation, assume the temperature of the air inside the vessel T remains unchanged, the no. of moles of air in each vessel, before they are connected, is given by,

For the 8L vessel, no. of moles of air inside n1 = where R is the Universal Gas Constant.8 x 30000/RT

For the 4.3L vessel, no. of moles of air inside n2 = 4.3 x 10000/RT

Hence, total mass (no. of moles) of air in the two vessles before connected = n1 + n2 = [(8 x 30000) + (4.3 x 10000)]/RT

Mass (no. of moles n) of air after the vessels are connected
n = (Pf)(8 + 4.3)/RT
where Pf is the final pressure after connection.
Using Law of Conservation of Mass, no. of moles of air in the two vessels before and after connection are the same.
i.e. n1 + n2 = n

[(8 x 30000) + (4.3 x 10000)]/RT = (Pf)(8 + 4.3)/RT
solve for Pf gives the final pressure = 23,008 psi.