An ideal gas is sealed within a container at a tempreture of 17 degree celcies and a pressure of 101KPa. The container is heated until the tempreture of the gas reaches 100 degree celcies. A valve in the container is then opened to allow gas to escape until the pressure falls back to 101KPa at 100 degree celcies. 1) calculate the pressure in the gas just before the valve is opened. 2) calculate the fraction of the initial mass of gas that was lost as a result of opening the valve.

Question

An ideal gas is sealed within a container at a tempreture of 17 degree celcies and a pressure of 101KPa. The container is heated until the tempreture of the gas reaches 100 degree celcies. A valve in the container is then opened to allow gas to escape until the pressure falls back to 101KPa at 100 degree celcies. 1) calculate the pressure in the gas just before the valve is opened. 2) calculate the fraction of the initial mass of gas that was lost as a result of opening the valve.

Answer 1

To solve this problem, we can use the ideal gas law, which states:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.

1) To calculate the pressure just before the valve is opened, we need to use the ideal gas law equation before and after the temperature change. Let's assume the volume and the number of moles of the gas remain constant throughout.

Before heating the gas:
P1 = 101 kPa
T1 = 17 °C = 17 + 273.15 = 290.15 K

After heating the gas:
T2 = 100 °C = 100 + 273.15 = 373.15 K

Since the volume (V) and the number of moles (n) remain constant, we can write:

P1/T1 = P2/T2

Solving for P2:

P2 = (P1 * T2) / T1
P2 = (101 kPa * 373.15 K) / 290.15 K
P2 ≈ 129.23 kPa

So, the pressure in the gas just before the valve is opened is approximately 129.23 kPa.

2) To calculate the fraction of the initial mass of gas lost, we need to assume that the gas behaves ideally and the initial and final conditions of the gas (before and after opening the valve) are at the same pressure and temperature.

Since the pressure is initially 101 kPa and finally returns to the same pressure, we can calculate the initial and final volumes using the ideal gas law equation:

P1 * V1 = n * R * T1
P2 * V2 = n * R * T2

Since the number of moles (n) and the ideal gas constant (R) remain constant, we can divide these equations to find the ratio of initial and final volumes:

V1 / V2 = T1 / T2
V1 / V2 = 290.15 K / 373.15 K
V1 / V2 ≈ 0.7778

The ratio of volumes represents the fraction of the initial gas mass that is lost. Therefore, the fraction of the initial mass lost is approximately 0.7778.

Please note that in this calculation, we assume the gas behaves ideally and the container is rigid, meaning that the volume does not change during the process.