Question

Температура газів, що утворюються при згорянні палива в циліндрах двигуна автомобіля, 800 °С. Температура вихлопних газів 80 °С. Витрата бензину на 100 км шляху при швидкості 90 км/год дорівнює 10 л. Яку потужність міг би розвинути двигун, якби він був ідеальною тепловою машиною, що працює з максимально можливим коефіцієнтом корисної дії?

Answer 1

Дано:

t₁ = 800⁰C T₁ = 273 + 800 = 1073 К

t₂ = 80⁰C T₁ = 273 + 80 = 353 К

S = 100 км = 100 000 м

v = 90 км/ч = 25 м/с

V = 10 л = 10·10⁻³ м³

ρ = 700 кг/м³ - плотность бензина

q = 46,2·10⁶ Дж/кг - теплота сгорания бензина

_____________

N - ?

1)

Максимальный КПД:

η = (T₁ - T₂) / T₁ = (1073 - 353) / 1073 ≈ 0,67

2)

Время движения автомобиля:

t = S / v = 100000 / 25 = 4 000 с

3)

Масса сгоревшего бензина:

m = ρ·V = 700·10·10⁻³ = 7 кг

4)

Количество теплоты при сгорании бензина:

Q = q·m = 46,2·10⁶·7 ≈ 3,2·10⁸ Дж

5)

Мощность автомобиля при 100% КПД

N₀ = Q/t = 3,2·10⁸ / 4000 ≈ 81 кВт

6)

Реальная мощность:

N =η· N₀ = 0,67·81 ≈ 54 кВт

Answer 2

Calculation of Engine Power

To calculate the power that the engine could develop if it were an ideal heat engine operating with the maximum possible efficiency, we can use the following formula:

Power = (Fuel consumption rate * Energy content of fuel) / (Time taken to cover the distance)

Let's break down the given information and calculate the engine power.

1. Fuel consumption rate: The fuel consumption rate is given as 10 liters per 100 kilometers.

2. Energy content of fuel: The energy content of gasoline can vary, but for this calculation, we will assume an average value of 34.2 megajoules per liter.

3. Time taken to cover the distance: To calculate the time taken to cover the distance, we need to know the speed at which the distance is covered. The given information states that the speed is 90 kilometers per hour.

Now, let's calculate the engine power:

Fuel consumption rate = 10 liters per 100 kilometers

Energy content of fuel = 34.2 megajoules per liter

Time taken to cover the distance = Distance / Speed

Given that the distance is 100 kilometers and the speed is 90 kilometers per hour, the time taken to cover the distance is:

Time taken to cover the distance = 100 kilometers / 90 kilometers per hour = 1.11 hours

Now, we can calculate the engine power using the formula mentioned above:

Power = (Fuel consumption rate * Energy content of fuel) / (Time taken to cover the distance)

Power = (10 liters / 100 kilometers * 34.2 megajoules per liter) / 1.11 hours

Calculating this expression gives us the engine power.

Please note that the given information does not provide the efficiency of the engine. To calculate the power of an ideal heat engine, we need to know the efficiency. Without the efficiency value, we cannot provide an accurate calculation of the engine power.