Question

3-31 10-kg of r-134a fill a 1.348-m3 rigid container at an initial temperature of -40 c. the container is then heated until the pressure is 200 kpa. determine the final temperature and pressure.

Answer 1

To determine the final temperature and pressure, we can use the ideal gas law equation PV = nRT. After converting the initial temperature to Kelvin, we can rearrange the equation to solve for the final temperature. Similarly, we can solve for the final pressure using the same equation.

Step-by-step explanation:

To solve this problem, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

First, we need to convert the initial temperature of -40°C to Kelvin. To do this, we use the equation K = °C + 273.15. Thus, the initial temperature is 233.15K.

We can rearrange the ideal gas law equation to solve for the final temperature. Since the initial and final volume and number of moles are the same, we have:

(P1/T1) = (P2/T2)

Substituting the values we have, we get:

(200 kPa)/(233.15 K) = P2/T2

Now, we can solve for T2:

(200 kPa)/(233.15 K) = P2/T2

T2 = (233.15 K x 200 kPa) / P2

Using a similar approach, we can solve for the final pressure. Since the initial and final volume and temperature are the same, we have:

(P1/T1) = (P2/T2)

Substituting the values we have, we get:

(200 kPa)/(233.15 K) = P2/(-40 + 273.15 K)

Now, we can solve for P2:

(200 kPa)/(233.15 K) = P2/(233.15 K)

P2 = 200 kPa x (233.15 K / 273.15 K)

Answer 2

To find the final temperature and pressure, we can use the ideal gas law equation. We convert the initial temperature of -40°C to Kelvin and calculate the initial number of moles using the given mass. By substituting these values into the equation and solving for R, we find the value of R to be approximately 0.087 kPa·m^3/(mol·K). Then, using the final volume, number of moles, and the value of R, we can calculate the final temperature to be approximately 548.2 K.

Step-by-step explanation:

To determine the final temperature and pressure, we can use the ideal gas law equation: PV = nRT.
First, let's convert the initial temperature of -40°C to Kelvin by adding 273.15: -40 + 273.15 = 233.15 K.
Then, we can calculate the initial number of moles using the given mass of 10 kg and the molar mass of R-134a, which is approximately 102.03 g/mol. 10,000 g / 102.03 g/mol = 98.02 mol.
Substituting the values into the equation: (200 kPa)(1.348 m^3) = (98.02 mol)(R)(233.15 K), we can solve for R to be approximately 0.087 kPa·m^3/(mol·K).
Now, we can use the final volume of 1.348 m^3, the number of moles of 98.02 mol, and the value of R to calculate the final temperature: (200 kPa)(1.348 m^3) = (98.02 mol)(0.087 kPa·m^3/(mol·K))(T). Solving for T gives us T ≈ 548.2 K.