Question

Cylinder of (300 L) containing Oxygen under pressure of (3.1 Mpa) and temperature of (18°C), valve is opened and the gas is used. The pressure of the remained oxygen (1.7 Mpa) and temperature of (15°C), after closing the valve the temperature of the gas returned to its initial value. Find the heat transferred if the density of Oxygen at (0°C) and pressure (0.101325 Mpa) is (1.429 kg/m³), and γ = 1.4.

Answer 1

The heat transferred is 0 kJ.

Step-by-step explanation:

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

PV = nRT

Where:

• P = pressure
• V = volume
• n = number of moles
• R = ideal gas constant
• T = temperature

We need to calculate the number of moles of oxygen gas present in the cylinder initially. Rearranging the equation, we have:

n = PV / RT

Substituting the given values:

n = (3.1 Mpa * 300 L) / ((0.101325 Mpa * 1.429 kg/m³) * (18 + 273) K)

n = 31 moles

Now, we can calculate the heat transferred using the formula:

q = mcΔT

Where:

• q = heat transferred
• m = mass
• c = specific heat capacity
• ΔT = change in temperature

Since the temperature returned to its initial value, ΔT = 0. Substituting the values, we have:

q = (31 moles * 32 g/mol) * (0.4 kJ/kg·K) * 0 K

q = 0 kJ

Therefore, the heat transferred is 0 kJ.