Question

Helium contained in a closed, rigid tank, initially at 50°C, 5 bar, and a volume of 2 m3, is heated to a final pressure of 8 bar. Assume the ideal gas model for the helium. Kinetic and potential energy effects can be ignored.

(a) For an ideal gas in a closed system undergoing a constant volume process:
(b) Reducing the closed system energy balance for this process, the heat transfer per unit mass can be evaluated as:
(c) Determine the mass of the helium, in kg.

Answer 1

The mass of helium in the tank is found by using the ideal gas law equation PV = nRT. By knowing the initial state of the gas and converting the appropriate values to SI units, the number of moles and subsequently the mass can be determined.

Step-by-step explanation:

The problem involves determining the mass of helium in a rigid tank that has undergone a constant volume heating process, while assuming helium behaves as an ideal gas. To calculate the mass, one can use the ideal gas law equation, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

The initial state of the helium is given as P1 = 5 bar and T1 = 50°C. We need to convert the temperature to Kelvin by adding 273.15 to the Celsius temperature, giving T1 = 323.15 K. The volume V of the tank is 2 m3. Plugging in the values and solving for n, and since the molar mass of helium (He) is 4.00 g/mol, the mass m can be calculated as m = n × molar mass.

To find the mass in kilograms, one must also convert grams to kilograms by dividing by 1000.