A heat engine absorbs 126 kcal of heat and exhausts 77 kcal of heat in each cycle. Calculate the efficiency (as a percentage)
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 calculate the efficiency of a heat engine, you can use the formula:
Efficiency = (Heat input - Heat output) / Heat input
For the first scenario, where the heat engine absorbs 126 kcal and exhausts 77 kcal:
Efficiency = (126 kcal - 77 kcal) / 126 kcal = 49 kcal / 126 kcal = 0.3889
To express it as a percentage, you can multiply by 100:
Efficiency = 0.3889 * 100 = 38.89%
For the second scenario, where the heat engine operates in a Carnot Cycle between temperatures of 266 °C and 115 °C and absorbs 4250 cal:
The efficiency of a Carnot Cycle can be calculated using the formula:
Efficiency = 1 - (T2 / T1)
Where T1 is the absolute temperature at the high temperature reservoir and T2 is the absolute temperature at the low temperature reservoir.
First, let's convert the given temperatures from Celsius to Kelvin:
T1 = 266 °C + 273.15 = 539.15 K
T2 = 115 °C + 273.15 = 388.15 K
Now we can substitute the values into the formula:
Efficiency = 1 - (388.15 K / 539.15 K)
Efficiency = 1 - 0.7193
Efficiency = 0.2807
To express it as a percentage, multiply by 100:
Efficiency = 0.2807 * 100 = 28.07%
Therefore, the efficiency of the ideal gas heat engine in a Carnot Cycle is 28.07%.
To calculate the efficiency of a heat engine, you can use the formula:
Efficiency = (Work output / Heat input) * 100
For the first question, we are given the heat input and heat output values. We can start by calculating the work output.
Work output = Heat input - Heat output
Work output = 126 kcal - 77 kcal = 49 kcal
Now we can calculate the efficiency:
Efficiency = (Work output / Heat input) * 100
Efficiency = (49 kcal / 126 kcal) * 100 ≈ 38.89%
Therefore, the efficiency of the heat engine in the first question is approximately 38.89%.
Moving on to the second question, we are given the heat input value and the temperatures at which the engine operates.
The efficiency of a Carnot Cycle can be calculated using the formula:
Efficiency = 1 - (Tc / Th)
Where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.
In this case, Tc = 115°C and Th = 266°C.
Efficiency = 1 - (115 / 266)
Efficiency ≈ 0.567
To convert this to a percentage, we multiply by 100:
Efficiency ≈ 0.567 * 100 = 56.7%
Therefore, the efficiency of the ideal gas heat engine in the second question is approximately 56.7%.