2.1 Exercise 22

A high-pressure gas cylinder contains 50.0 L of toxic gas at a pressure of $1.40 \times 10^{7} \text{N}/\text{m}^{2}$ and a temperature of $25.0 °\text{C}$. The cylinder is cooled to dry ice temperature $\left(−78.5 ° \text{C}\right)$ to reduce the leak rate and pressure so that it can be safely repaired. (a) What is the final pressure in the tank, assuming a negligible amount of gas leaks while being cooled and that there is no phase change? (b) What is the final pressure if one-tenth of the gas escapes? (c) To what temperature must the tank be cooled to reduce the pressure to 1.00 atm (assuming the gas does not change phase and that there is no leakage during cooling)? (d) Does cooling the tank as in part (c) appear to be a practical solution?