A small research submarine with a volume of 1.2x10 ^5 L has an internal pressure of 1.0 atm and an internal temperature of 150°C. If the submarine descends to a depth where the pressure is 150 atm and the temperature is 30°C, what will the volume of the gas inside be if the hull of the submarine breaks?

1 Answer
Stefan V.
Dec 7, 2014

The answer is #573L#.

The best way to approach this problem is by using the combined gas law

#(P_1V_1)/T_1 = (P_2V_2)/T_2#, which relates temperature, pressure, and volume, assuming the number of moles remains constant. Knowing that

#P_1 = 1atm#, #T_1 = 273.15 + 150 = 423.15K#, #V_1 = 1.2* 10^5 L#, #P_2 = 150 atm#, and #T_2 = 303.15K#, we get

#V_2 = P_1/P_2 * T_2/T_1 * V_1 = 1/150 * (303.15)/(423.15) * 1.2 * 10^5 = 573L#

Notice how both a significant increase in pressure and an important drop in temperature contributed to the massive drop in volume the submarine underwent.

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