Final answer:
The dial of the steam gauge must read at least a) 6% above the safety valve setting, as indicated by the principles of the ideal gas law and the proportional relationship between temperature and pressure.
Step-by-step explanation:
The question pertains to the principles of steam pressure and safety mechanisms involved in operating machinery like a steam engine. In industrial and engineering contexts, it is important that the dial of the steam gauge reads at a level above the safety valve setting to allow for a margin of safety and ensure that the system operates within safe limits.
From the discussion provided, it notes that there is a 6% increase in final pressure compared to the original pressure due to the increase in temperature, referencing the ideal gas law. Therefore, the minimum percentage by which the dial of the steam gauge must read above the safety valve setting would be 6%.