Question

В закрытом сосуде емкости 0,6 м^3 содержится воздух при давлении 0,5 МПа и температуре 20С.В результате охлождения сосуда воздух содержащийся в нем теряет 105кДж.Принимая теплоемкость воздуха постояннной,определить какое давление и какая температура устанавливается после этого в сосуде

Answer 1

Так как процесс происходит при постоянном объеме то работа не совершается
Q = 5/2*Ню*R*ΔT (коэффициент 5/2 потому что воздух в основном двухатомный газ)
(но возможно и другое решение если в вашем задачнике дана теплоемкость воздуха при постоянном объеме)

P1*V1= ню*R*T1
ню*R=P1*V1/T1
Q==2,5*P1*V1*ΔT/T1
ΔT=Q*T1/2,5*P1/V1
После этого найдете T2= T1+ΔT
После этого из уравнения состояния
P1/T1=P2/T2
P2=P1*T2/T1
осталось сделать вычисления, но нет у меня времени  дела.....
извините....

Answer 2

Given Information:

- Volume of the container: 0.6 m^3 - Initial pressure of the air: 0.5 MPa - Initial temperature of the air: 20°C - Heat lost by the air: 105 kJ

Approach:

To determine the final pressure and temperature of the air in the container after cooling, we can use the ideal gas law and the first law of thermodynamics.

Ideal Gas Law:

The ideal gas law states that the pressure, volume, and temperature of a gas are related by the equation: PV = nRT, where: - P is the pressure of the gas - V is the volume of the gas - n is the number of moles of the gas - R is the ideal gas constant - T is the temperature of the gas

First Law of Thermodynamics:

The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. Mathematically, it can be expressed as: ΔU = Q - W, where: - ΔU is the change in internal energy - Q is the heat added to the system - W is the work done by the system

Since the problem states that the heat lost by the air is 105 kJ, we can assume that the heat lost is equal to the change in internal energy of the air.

Solution:

1. Convert the initial pressure from MPa to Pa: - 0.5 MPa = 0.5 * 10^6 Pa

2. Convert the initial temperature from Celsius to Kelvin: - T_initial = 20°C + 273.15 = 293.15 K

3. Use the ideal gas law to find the number of moles of air: - Rearrange the ideal gas law equation to solve for n: n = PV / RT - Substitute the given values: n = (0.5 * 10^6 Pa * 0.6 m^3) / (8.314 J/(mol·K) * 293.15 K)

4. Calculate the change in internal energy: - ΔU = Q = -105 kJ

5. Use the first law of thermodynamics to find the final temperature: - ΔU = Q - W - Since the problem states that the heat lost is equal to the change in internal energy, we can write: ΔU = -105 kJ - Rearrange the equation to solve for the work done by the system: W = Q - ΔU - Assume no work is done by the system, so W = 0 - Substitute the values: 0 = -105 kJ - 0 - Solve for the final temperature.

6. Use the ideal gas law to find the final pressure: - Rearrange the ideal gas law equation to solve for P: P = nRT / V - Substitute the values: P = (n * R * T_final) / V

Calculation:

Let's calculate the final temperature and pressure using the given information and the equations mentioned above.

1. Convert the initial pressure from MPa to Pa: - 0.5 MPa = 0.5 * 10^6 Pa

2. Convert the initial temperature from Celsius to Kelvin: - T_initial = 20°C + 273.15 = 293.15 K

3. Calculate the number of moles of air: - n = (0.5 * 10^6 Pa * 0.6 m^3) / (8.314 J/(mol·K) * 293.15 K)

4. Calculate the change in internal energy: - ΔU = -105 kJ

5. Calculate the final temperature using the first law of thermodynamics: - ΔU = Q - W - 0 = -105 kJ - 0 - Solve for the final temperature.

6. Calculate the final pressure using the ideal gas law: - P = (n * R * T_final) / V

Answer:

The final pressure and temperature in the container after cooling will depend on the specific values of the number of moles of air and the final temperature. Please provide the specific values for a more accurate calculation.