An ideal gas heat engine operates in a Carnot Cycle between temperatures of 266 and 115°C. It absorbs 4250 cal per cycle at 266°C. What is its efficiency as a percentage
To find the efficiency of an ideal gas heat engine operating in a Carnot Cycle, we can use the formula:
Efficiency = 1 - (T2 / T1)
where T1 is the absolute temperature at which heat is absorbed and T2 is the absolute temperature at which heat is rejected.
First, let's convert the temperatures from Celsius to Kelvin by adding 273.15 to each value:
T1 = 266 + 273.15 = 539.15 K
T2 = 115 + 273.15 = 388.15 K
Now we can calculate the efficiency:
Efficiency = 1 - (T2 / T1)
Efficiency = 1 - (388.15 / 539.15)
Efficiency = 1 - 0.720
Efficiency = 0.280
To express the efficiency as a percentage, we multiply by 100:
Efficiency = 0.280 * 100
Efficiency = 28%
Therefore, the efficiency of the ideal gas heat engine is 28%.
To find the efficiency of the Carnot cycle, we can use the formula:
Efficiency = (1 - T2/T1) * 100
Where:
T2 is the lower temperature in Kelvin
T1 is the higher temperature in Kelvin
First, we need to convert the temperatures from Celsius to Kelvin.
T1 = 266 + 273 = 539 K
T2 = 115 + 273 = 388 K
Next, we can substitute the values into the formula and calculate the efficiency:
Efficiency = (1 - 388/539) * 100
Efficiency = (1 - 0.719) * 100
Efficiency = (0.281) * 100
Efficiency = 28.1%
Therefore, the efficiency of the Carnot cycle in this case is 28.1%.