Question

Совершая цикл Карно, газ получил от нагревателя 2 ккал теплоты и произвел работу 1500 Дж. Температура холодильника 0С. Определить температуру нагревателя.

Answer 1

Q1=2*4186=8372 Дж
кпд=A/Q1=1500/8372=0,18
кпд=T1-T2/T1
T1=T2/(1-кпд)=273/(1-0,18)=333 K

Answer 2

Calculation of the Temperature of the Heater in a Carnot Cycle

To determine the temperature of the heater in a Carnot cycle, we can use the equation for the efficiency of a Carnot cycle:

Efficiency = 1 - (Temperature of the Cold Reservoir / Temperature of the Hot Reservoir)

In this case, the temperature of the cold reservoir is given as 0°C. Let's assume this temperature is in Kelvin, so the temperature of the cold reservoir is 273 K.

We are also given that the gas received 2 kcal of heat from the heater and produced 1500 J of work. To convert kcal to Joules, we can use the conversion factor: 1 kcal = 4184 J.

Let's calculate the efficiency of the Carnot cycle using the given information:

Efficiency = 1 - (Temperature of the Cold Reservoir / Temperature of the Hot Reservoir)

1500 J = Efficiency * 2 kcal * 4184 J/kcal

Simplifying the equation:

Efficiency = 1500 J / (2 kcal * 4184 J/kcal)

Now, let's solve for the temperature of the hot reservoir:

Efficiency = 1 - (273 K / Temperature of the Hot Reservoir)

Substituting the calculated efficiency value:

1500 J / (2 kcal * 4184 J/kcal) = 1 - (273 K / Temperature of the Hot Reservoir)

Simplifying the equation:

Temperature of the Hot Reservoir = 273 K / (1 - (1500 J / (2 kcal * 4184 J/kcal)))

Now, let's calculate the temperature of the hot reservoir using the given values:

Temperature of the Hot Reservoir = 273 K / (1 - (1500 J / (2 kcal * 4184 J/kcal)))

Calculating the value:

Temperature of the Hot Reservoir ≈ 273 K / (1 - (1500 J / (2 * 4184 J/kcal)))

Temperature of the Hot Reservoir ≈ 273 K / (1 - (1500 J / 8368 J))

Temperature of the Hot Reservoir ≈ 273 K / (1 - 0.1794)

Temperature of the Hot Reservoir ≈ 273 K / 0.8206

Temperature of the Hot Reservoir ≈ 332.68 K

Therefore, the temperature of the heater in the Carnot cycle is approximately 332.68 K.

Please note that the above calculation assumes ideal conditions and does not take into account any losses or inefficiencies in the Carnot cycle.