The equation of state for 5g of oxygen at a pressure P and temperature T, when occupying a volume V, will be :-

Question

A real gas within a closed chamber at \( 27^\circ \text{C} \) undergoes the cyclic process as shown in the figure. The gas obeys the equation \( PV^3 = RT \) for the path A to B. The net work done in the complete cycle is (assuming \( R = 8 \, \text{J/molK} \)):

Answer 1

To determine the equation of state for 5g of oxygen at a given pressure \(P\), temperature \(T\), and volume \(V\), we start with the ideal gas equation:

PV = nRT

Here, \(n\) is the number of moles, \(R\) is the universal gas constant, \(P\) is the pressure, \(V\) is the volume, and \(T\) is the temperature.

First, we need to calculate the number of moles \(n\) of oxygen. The molar mass of oxygen (O₂) is approximately 32 g/mol.

Thus, the number of moles \(n\) is given by:

n = \frac{\text{mass of oxygen}}{\text{molar mass of oxygen}} = \frac{5}{32}

Substitute this value into the ideal gas equation:

PV = \left(\frac{5}{32}\right)RT

By comparing this with the given options, the correct equation of state is:

Correct Answer: PV = \left(\frac{5}{32}\right)RT

Explanation: The equation reflects the proportion of the mass of oxygen to its molar mass, incorporated with the ideal gas law. This results in calculating the number of moles, which gives us the correct formulation of the equation.

Answer 2