Chapter 3: Q28E (page 641)

The engine of a Ferrari F355 F1 sports car takes in air at $20 ° C$ and 1 atm and compresses it adiabatically to 0.09 times the original volume. The air may be treated as an ideal gas with $γ = 1.4$ . (a) Draw a pV-diagram for this process. (b) Find the final temperature and pressure.

Short Answer

Expert verified

b. The final temperature ans pressure is $T_{2} = 768 K$ and $P_{2} = 29 a t m$ respectively.

Step by step solution

Draw the pV diagram of the process

For the adiabatic compression process, the volume decreases while the pressure increases. The graph will be as follows

Calculate the final temperature

For an adiabatic process, the relation between temperature and volume is $T_{1} V_{1}^{γ - 1} = T_{2} V_{2}^{γ - 1}$ and between pressure and volume is $P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$ .

Here, $v_{1}$ and $v_{2}$ is the initial and final volume respectively. Next $T_{1}$ and $T_{2}$ is the initial and final temperature respectively. And $P_{1}$ and $P_{2}$ is the initial and final pressure respectively.

Consider the given data as below.

$V_{2} = 0.09 V_{1}$ .

Define the final temperature as below.

$T_{2} = T_{1} {(\frac{V_{1}}{V_{2}})}^{γ - 1} = 293 {(\frac{V_{1}}{0.09 V_{1}})}^{14 - 1} = 768 K$

Calculate the final pressure

Define the final pressure as below.

$P_{2} = P_{1} {(\frac{V_{1}}{V_{2}})}^{γ} = 1 \times {(\frac{V_{1}}{0.09 V_{1}})}^{14} = 29 a t m$

Result:

The final temperature and pressure is $T_{2} = 768 K$ and $P_{2} = 29 a t m$ respectively.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

The engine of a Ferrari F355 F1 sports car takes in air at $20 ° C$ and 1 atm and compresses it adiabatically to 0.09 times the original volume. The air may be treated as an ideal gas with $γ = 1.4$ . (a) Draw a pV-diagram for this process. (b) Find the final temperature and pressure.

Short Answer

Step by step solution

Draw the pV diagram of the process

Calculate the final temperature

Calculate the final pressure

Result:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Space Physics

Further Mechanics and Thermal Physics

Famous Physicists

Electromagnetism

Fields in Physics

Rotational Dynamics

Study anywhere. Anytime. Across all devices.

The engine of a Ferrari F355 F1 sports car takes in air at 20°C and 1 atm and compresses it adiabatically to 0.09 times the original volume. The air may be treated as an ideal gas with γ=1.4 . (a) Draw a pV-diagram for this process. (b) Find the final temperature and pressure.

Short Answer

Step by step solution

Draw the pV diagram of the process

Calculate the final temperature

Calculate the final pressure

Result:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Space Physics

Further Mechanics and Thermal Physics

Famous Physicists

Electromagnetism

Fields in Physics

Rotational Dynamics

Study anywhere. Anytime. Across all devices.

The engine of a Ferrari F355 F1 sports car takes in air at $20 ° C$ and 1 atm and compresses it adiabatically to 0.09 times the original volume. The air may be treated as an ideal gas with $γ = 1.4$ . (a) Draw a pV-diagram for this process. (b) Find the final temperature and pressure.