Question 1

The National Grid is supplied mainly from thermal power stations which have overall efficiencies of up to about $38%38\%$ .

Table 1 shows the average power requirements of a large-scale industrial distillery.

Table 1

Requirement	Average power / MW
For driving grain mills, mash tun stirrers, centrifuges, and refrigeration compressors	19
For boiling wort, steam distillation, and bottle sterilization	62
For running automation systems, office services, and warehouse lighting	5

The distillery can either:

purchase all of its electrical power from the National Grid and burn gas locally in boilers to meet its heating demand, or
install an on-site biogas-driven turbine as part of a combined heat and power (CHP) scheme. The turbine has a maximum electrical generator output of $MW28\text{ MW}$ and an electrical efficiency of $30%30\%$ . High-temperature exhaust gases from the turbine are captured to produce steam for the heating requirements.

The directors of the distillery are evaluating whether to proceed with the CHP installation.

Explain, with reference to the provided data and physical principles, the advice you would give them.

In your answer you should:

explain why the maximum theoretical efficiency of any heat engine is fundamentally limited to well below $100%100\%$
use the numerical data to quantitatively compare the two operating options.