Question

Air at 300 K300 \mathrm{~K}300 K and 100kPa100 \mathrm{kPa}100kPa and a specific heat ratio of 1.41.41.4 undergoes an isentropic compression to 1MPa1 \mathrm{MPa}1MPa. What is the final air temperature in Kelvin after the compression?

Answer 1

After an isentropic compression from 100 kPa to 1 MPa, the final temperature of air with an initial temperature of 300 K and a specific heat ratio of 1.4 is approximately 792 Kelvin.

Step-by-step explanation:

To find the final temperature of air after an isentropic compression, you can use the following relationship, which relates temperature and pressure for an ideal gas undergoing this type of compression:

T2 = T1 \times (P2/P1)^{((γ-1)/γ)}

Where:

• T1: Initial temperature
  
• T2: Final temperature
  
• P1: Initial pressure
  
• P2: Final pressure
  
• γ (gamma): Specific heat ratio
  

Given that the initial temperature (T1) is 300 K, the initial pressure (P1) is 100 kPa, the final pressure (P2) is 1 MPa (1000 kPa), and the specific heat ratio (gamma) is 1.4, you can substitute these values into the equation to obtain the final temperature (T2).

T2 = 300 K \times (1000 kPa / 100 kPa)^{(1.4-1)/1.4}

Doing the math:

T2 = 300 K \times 10^{0.4/1.4}

T2 ≈ 300 K \times 2.639

T2 ≈ 792 K

Therefore, the final temperature of air after the isentropic compression to 1MPa is approximately 792 Kelvin.