To determine the final pressure in a gas tank after cooling and leakage, calculations involving the combined gas law are necessary. The pressure and temperature changes used in these calculations will lead to conclusions about the practicality of the method used to lower the tank's pressure.
The question presented relates to thermodynamics and involves calculations to determine the final pressure in a gas tank after cooling and in scenarios of gas leakage, as well as finding necessary cooling temperatures to reach certain pressures.
For part (a), the final pressure after cooling to dry ice temperature can be found using the combined gas law, which relates the pressure, volume, and temperature of a gas. Assuming negligible leakage and no phase change, the final pressure of the gas can be calculated using the initial and final temperatures and the initial pressure.
For part (b), if one-tenth of the gas escapes, the volume of the remaining gas will be 90% of the initial volume. The final pressure can again be computed using the combined gas law or directly by understanding that a decrease in the amount of gas leads directly to a proportional decrease in pressure for a constant volume and temperature.
For parts (c) and (d), we would need to compute the temperature to which the tank must be cooled to achieve a pressure of 1 atm, still assuming no leakage or phase change. We can then discuss whether or not cooling as a method to lower the pressure is a practical solution based on the logistics of reaching the required temperatures and maintaining safety.