Question

Визначити ККД циклу Карно, якщо температура нагрівника і холодильника відповідно дорівнюють 200°С і 15°C. Наскільки треба підвищити температуру нагрівника, щоб ККД циклу зріс удвічі?

Answer 1

Ответ:

1321К

Объяснение:

КПД по циклу Карно n1=T1-T2/T1=0.391 или 39.1%

Температура холодильника осталась неизменной а КПД увеличилось в 2 раза,тогда:

2n1=T'-T2/T', где T' это повышенная температура нагревателя,считаем T' = 1321K

Answer 2

Calculation of Carnot Cycle Efficiency

To determine the Carnot cycle efficiency (η) and the required increase in the temperature of the heat source (nagrivnik) to double the efficiency, we can use the formula for the Carnot cycle efficiency:

η = 1 - (Tc/Th)

Where: - η is the Carnot cycle efficiency, - Tc is the temperature of the cold reservoir (holodilnik), and - Th is the temperature of the hot reservoir (nagrivnik).

Given that the temperature of the heat source (nagrivnik) is 200°C and the temperature of the cold reservoir (holodilnik) is 15°C, we can substitute these values into the formula to calculate the initial Carnot cycle efficiency.

Initial Carnot cycle efficiency (η_initial): η_initial = 1 - (15/200)

To find the required increase in the temperature of the heat source (nagrivnik) to double the efficiency, we need to calculate the new Carnot cycle efficiency when the efficiency is doubled.

New Carnot cycle efficiency (η_new): η_new = 2 * η_initial

Now, let's calculate the initial Carnot cycle efficiency and the required increase in the temperature of the heat source.

Calculation:

Given: - Temperature of the heat source (nagrivnik) = 200°C - Temperature of the cold reservoir (holodilnik) = 15°C

Step 1: Calculate the initial Carnot cycle efficiency (η_initial):

η_initial = 1 - (15/200) η_initial = 1 - 0.075 η_initial = 0.925

Step 2: Calculate the new Carnot cycle efficiency (η_new):

η_new = 2 * η_initial η_new = 2 * 0.925 η_new = 1.85

Step 3: Calculate the required increase in the temperature of the heat source (nagrivnik):

Let's assume the required increase in temperature is ΔT.

η_new = 1 - (15/200+ΔT) 1.85 = 1 - (15/200+ΔT)

Solving for ΔT:

15/200+ΔT = 1 - 1.85 15/200+ΔT = -0.85

ΔT = (-0.85 - 15/200) * 200 ΔT = (-0.85 - 0.075) * 200 ΔT = -0.925 * 200 ΔT = -185

The required increase in the temperature of the heat source (nagrivnik) to double the Carnot cycle efficiency is -185°C.

Please note that a negative value for the required increase in temperature indicates that the temperature of the heat source (nagrivnik) needs to be decreased by 185°C to achieve a doubling of the Carnot cycle efficiency.

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