Question

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?

Answer 1

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.