Melissa’s backup oxygen tank reads 900 mmHg while on her boat, where the temperature is 27 degrees Celsius. When she dives down to the bottom of an unexplored methane lake on a recently-discovered moon of Neptune, the temperature will drop down to -183 de

The pressure in Melissa's backup oxygen tank can be calculated using the combined gas law, which states that: {eq}frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} {/eq} where {eq}P_1,V_1,T_1{/eq} are the initial pressure, volume, and temperature, and {eq}P_2,V_2,T_2{/eq} are the final pressure, volume, and temperature. We know that her backup oxygen tank initially reads {eq}900 rm{mmHg} {/eq} at a temperature of 27 degrees Celsius, which is 300 Kelvin. When she dives down to the bottom of the methane lake, the temperature drops to -183 degrees Celsius, which is 90 Kelvin. Let's plug these values into the combined gas law: {eq}frac{(900 rm{mmHg})(V_1)}{(300 rm{K})} = \frac{(P_2)(V_1)}{(90 rm{K})} {/eq} Solving for {eq}P_2{/eq} gives us: {eq}P_2 = \frac{(900 rm{mmHg})(90 rm{K})}{300 rm{K}} = 270 rm{mmHg} {/eq} So the pressure in Melissa's backup oxygen tank at the bottom of the methane lake would be 270 mmHg, assuming that the volume of the tank remains constant. This is significantly lower than the initial pressure of 900 mmHg, which means that the oxygen supply in her tank would be depleted much faster at the lower temperature and pressure.