## Answer:

**Part (a) – Calculate V1, V2, and P2**

For a reversible process at constant temperature, we can use the ideal gas law to relate the pressure and volume of the gas:

```
PV = nRT
```

where:

- P is the pressure (kPa)
- V is the volume (m³)
- n is the number of moles of gas
- R is the gas constant (8.314 J/mol·K)
- T is the temperature (K)

Since the temperature is constant, we can write:

```
P1V1 = P2V2
```

We are given that P1 = 586 kPa and V1 = 1.134 m³/s. We can also calculate the number of moles of gas using the molar mass of the gas and the mass flow rate:

```
n = m/M
```

where:

- m is the mass flow rate (kg/s)
- M is the molar mass (kg/mol)

For a specific gas, we can find the molar mass from the specific heat capacities using the relationship:

```
cp - cv = R
```

Solving for R, we get:

```
R = cp - cv = 2.232 kJ/kg·K - 1.713 kJ/kg·K = 0.519 kJ/kg·K
```

Using the given values, we can calculate the number of moles of gas:

```
n = m/M = (1.134 kg/s) / (M kg/mol)
```

We need to find the molar mass (M) in order to proceed.

**Part (b) – Calculate the work and Q**

For a reversible process at constant temperature, the work done is equal to the heat transferred:

```
W = Q
```

We can calculate the work using the formula:

```
W = -PdV
```

where:

- W is the work (kJ)
- P is the pressure (kPa)
- V is the volume (m³)

Since the temperature is constant, we can write:

```
W = -P1V1 + P2V2
```

Using the values we have so far, we can calculate the work:

```
W = (-586 kPa)(1.134 m³) + (P2)(1.134 m³) = -662.46 kPa·m³ + 1.134P2 m³
```

To calculate the heat transferred (Q), we can use the formula:

```
Q = mcΔT
```

where:

- Q is the heat transferred (kJ)
- m is the mass (kg)
- c is the specific heat capacity (kJ/kg·K)
- ΔT is the change in temperature (K)

Since the temperature is constant, ΔT = 0, and therefore Q = 0.

**Part (c) – Calculate ∆S and ∆H**

For a reversible process at constant temperature, the entropy change can be calculated using the formula:

```
ΔS = nR ln(P2/P1)
```

where:

- ΔS is the entropy change (kJ/kg·K)
- n is the number of moles of gas
- R is the gas constant (kJ/mol·K)
- P1 is the initial pressure (kPa)
- P2 is the final pressure (kPa)

Using the values we have so far, we can calculate the entropy change:

```
ΔS = (n)(0.519 kJ/mol·K) ln((P2)/586 kPa)
```

We need to find the final pressure (P2) to complete the calculation.

The enthalpy change for a reversible process at constant temperature is zero:

`ΔH = 0`