Final answer:
The maximum theoretical efficiency for a heat engine operating between a high temperature of 300°C (573.15 K) and a low temperature of 27°C (300.15 K) is 47.63%, calculated using the Carnot efficiency formula.
Step-by-step explanation:
To calculate the maximum theoretical efficiency for a heat engine operating between two temperatures, we can use the efficiency formula derived from the Carnot cycle, which is given by:
\(\eta = 1 - \frac{T_{cold}}{T_{hot}}\)
Where \(\eta\) is the efficiency, \(T_{cold}\) is the cold reservoir temperature, and \(T_{hot}\) is the hot reservoir temperature. Temperatures must be in Kelvin.
First, convert the temperatures from Celsius to Kelvin:
\(T_{cold} = 27 \degree C + 273.15 = 300.15 K\)
\(T_{hot} = 300 \degree C + 273.15 = 573.15 K\)
Now, substitute these values into the efficiency formula:
\(\eta = 1 - \frac{300.15}{573.15}\)
\(\eta = 1 - 0.5237\)
So, the maximum theoretical efficiency is:
\(\eta = 0.4763\)
Or in percentage:
\(\eta = 47.63\%\)
This calculation assumes an ideal Carnot engine, which is a theoretical limit and cannot be achieved in practical engines; the actual efficiency will be lower due to various inefficiencies.