Question

A rigid tank contains 0.8 kg of steam at 10 MPa and 300°C. The volume of the tank is (a) 11 m³ (b) 21 m³ (c) 4.3 m³ (d) 1.1 m³ (e) 0.23 m³

Answer 1

The student's question about the volume of a tank with steam cannot be determined without additional information. Normally, equations like the ideal gas law or real gas law are used along with steam properties to find the answer.

Step-by-step explanation:

The student's question asks for the volume of a rigid tank containing steam at a specific temperature and pressure. The options provided are (a) 11 m³, (b) 21 m³, (c) 4.3 m³, (d) 1.1 m³, (e) 0.23 m³. Unfortunately, without additional information or a context that relates these values to the state of the steam, it's not possible to accurately determine which one of these volumes is correct for the given steam conditions.

Normally, to solve this, you'd use the properties of steam tables, ideal gas law or real gas law equations, depending on the properties of the steam and whether it's behaving as an ideal gas under the given conditions. To find the volume, we would normally use the formula:

V = (mRT)/(MP)

where V is volume in m³, m is mass in kg, R is the specific gas constant for steam, T is temperature in Kelvin, M is the molar mass of steam, and P is pressure in Pascal. However, as mentioned, we cannot solve this without additional data or context.

Answer 2

The volume of the tank is 21 m³.

We can solve this problem using the ideal gas law and the steam tables.

Identify the state of the steam:

At 10 MPa and 300°C, the steam is superheated. This means it's above the saturation temperature for the given pressure.

2. Choose the appropriate equation:

For superheated steam, we can use the ideal gas law with a correction factor called the Z factor:

PV = mZRT

where:

P is the pressure (10 MPa)

V is the volume (unknown)

m is the mass of the steam (0.8 kg)

Z is the compressibility factor for superheated steam

R is the gas constant for steam (0.461 kJ/ kg · K)

T is the temperature (300°C + 273.15 K = 573.15 K)

Find the Z factor:

The Z factor for superheated steam can be found from steam tables. At 10 MPa and 300°C, the Z factor is approximately 0.982.

Solve for the volume:

Rearranging the ideal gas law:

V = mZRT /P

V = (0.8 kg) * (0.982) * (0.461 kJ/kg · K) * (573.15 K) / (10 MPa)

V ≈ 20.9 m³

The closest answer choice is (b) 21 m³.

Question:

A rigid tank contains 0.8 kg of steam at 10 MPa and 300°C. The volume of the tank is

(a) 11 m³

(b) 21 m³

(c) 4.3 m³

(d) 1.1 m³

(e) 0.23 m³