How to find mass given pressure and temperature

In summary, the given problem involves finding the mass of steam in a 3-m3 rigid vessel at 10 MPa and 500 degC. The solution involves using a thermo-table to find the specific volume of superheated water at the given pressure and temperature. Then, using the equation V/v = m, the mass of the steam is calculated to be 91 kg.
  • #1
Connor Rawls
2
0

Homework Statement


A 3-m3 rigid vessel contains steam at 10 MPa and 500 degC. The mass of the steam is?

I know this question involves using a thermo-table, I'm just very confused on how to find mass from the given information.

Homework Equations


Maybe PV=nRT

The Attempt at a Solution


I guessed at the fact that the steam is superheated water, so from there I looked up the pressure table for exactly that. From the given 10MPa, I found that the specific volume at 500 degC is 0.032811 m^3/kg. I'm lost on how to get a mass from this. My only guess is to use a total volume, V, and divide V by the specific volume, v. [ V/v ]
 
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  • #2
I solved it. Apparently 3-m3 means a Volume of 3 m^3. From there I divided V/v = 3/0.032811 = 91 kg.
 

1. What is the formula for finding mass given pressure and temperature?

The formula for finding mass given pressure and temperature is m = (P * V) / (R * T), where m is the mass in kilograms, P is the pressure in Pascals, V is the volume in cubic meters, R is the gas constant (8.314 J/mol*K), and T is the temperature in Kelvin.

2. How do you convert units for pressure and temperature when using the formula?

When using the formula, it is important to ensure that all units are in the correct SI units. Pressure should be in Pascals (Pa) and temperature should be in Kelvin (K). If the pressure is given in another unit, it can be converted to Pa by using a conversion factor. If the temperature is given in Celsius (°C), it can be converted to Kelvin by adding 273.15.

3. Can the formula be used for any gas or does it only apply to certain types of gases?

The formula can be used for any gas as long as the conditions are within the ideal gas law. This means that the gas is at low pressure and high temperature, and the particles are not interacting with each other.

4. What are the limitations of using the formula to find mass?

The formula assumes that the gas is behaving ideally, which may not always be the case. Additionally, it only considers pressure and temperature, and does not take into account other factors such as density or molecular weight, which may affect the accuracy of the calculated mass.

5. Are there any other methods for finding mass given pressure and temperature?

Yes, there are other methods such as using the ideal gas law to calculate the number of moles and then converting to mass using the molar mass of the gas. Another method is to use the density of the gas at a given pressure and temperature to calculate the mass. However, the formula for finding mass using pressure and temperature is the most commonly used method.

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