What is the maximum theoretical efficiency of a steam engine operating between 60°C and 410°C?

Use the formula for the Carnot cycle efficiency.

Temperatures must be in kelvin.
T1 = 333K
T2 = 683 K

Carnot Efficiency = 1 - (T1/T2)

To find the maximum theoretical efficiency of a steam engine operating between two temperatures, we can use the Carnot efficiency formula. The Carnot efficiency represents the ideal maximum efficiency that any heat engine could achieve. It is given by the formula:

Efficiency = 1 - (T_cold / T_hot)

Where T_cold is the temperature of the heat sink (in Kelvin) and T_hot is the temperature of the heat source (in Kelvin).

To calculate the efficiency, we need to convert the temperatures from Celsius to Kelvin. The Kelvin temperature scale is related to Celsius through the equation:

Kelvin temperature = Celsius temperature + 273.15

Therefore, we need to convert 60°C to Kelvin:

T_cold = 60°C + 273.15 = 333.15 K

And convert 410°C to Kelvin:

T_hot = 410°C + 273.15 = 683.15 K

Now we can substitute these values into the Carnot efficiency formula:

Efficiency = 1 - (333.15 K / 683.15 K)

Simplifying the equation, we get:

Efficiency = 1 - 0.4876

Efficiency ≈ 0.5124 or 51.24%

Therefore, the maximum theoretical efficiency of the steam engine operating between 60°C and 410°C is approximately 51.24%.