Question

Газ находится в сосуде при давлении 2 МПа и температуре 27 °С. После нагревания на 50 °С в сосуде осталась половина газа. Определить установившееся давление.

Answer 1

$\frac{pV}{N}=kT$
температура с 300К стала 350, тоесть увеличилась на 7/6
Процесс изохорнь1й, так что и давление увеличилось на 7/6. 
Уменьшив количество на 1/2 и давление изменится на 1/2 и получаем
p * 7/6 * 1/2 = 2000000 * 7/12 = 1166666.67 ≈ 1.167 MПа


  

Answer 2

Calculation of the Final Pressure

To determine the final pressure of the gas after heating, we can use the ideal gas law 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 in Kelvin

In this case, we are given the initial pressure (2 MPa) and temperature (27 °C) of the gas, as well as the change in temperature (50 °C). We are also told that after heating, only half of the gas remains in the vessel.

To solve for the final pressure, we need to convert the temperatures to Kelvin and determine the number of moles of gas remaining.

Conversion of Temperatures to Kelvin

To convert the temperatures from Celsius to Kelvin, we use the formula:

T(K) = T(°C) + 273.15

Converting the initial temperature of 27 °C to Kelvin: T1 = 27 + 273.15 = 300.15 K

Converting the change in temperature of 50 °C to Kelvin: ΔT = 50 K

Calculation of the Number of Moles

To calculate the number of moles of gas remaining, we can use the ideal gas law equation rearranged to solve for n:

n = PV / RT

Since the volume of the gas remains constant, we can rewrite the equation as:

n1 / n2 = P1 / P2 * T2 / T1

Where: - n1 is the initial number of moles of gas - n2 is the final number of moles of gas - P1 is the initial pressure of the gas - P2 is the final pressure of the gas - T1 is the initial temperature of the gas in Kelvin - T2 is the final temperature of the gas in Kelvin

Since we are told that only half of the gas remains in the vessel after heating, we can substitute n2 = 0.5 * n1 into the equation:

n1 / (0.5 * n1) = P1 / P2 * T2 / T1

Simplifying the equation: 1 / 0.5 = P1 / P2 * T2 / T1

Calculation of the Final Pressure

Now we can solve for the final pressure (P2):

P2 = P1 * T2 / T1 * 0.5

Substituting the given values: P1 = 2 MPa = 2 * 10^6 Pa T1 = 300.15 K T2 = 300.15 K + 50 K = 350.15 K

P2 = (2 * 10^6 Pa) * (350.15 K / 300.15 K) * 0.5

Calculating the final pressure: P2 = 2.33 * 10^6 Pa

Therefore, the final pressure of the gas after heating is 2.33 MPa.

Conclusion

After heating the gas in the vessel, the final pressure is 2.33 MPa.