Chapter 19: Q. 30 (page 544)

A gas cylinder holds 0.10 mol of O2 at 150 $°$ C and a pressure
of 3.0 atm. The gas expands adiabatically until the volume is doubled.
What are the final (a) pressure and (b) temperature?

Short Answer

Expert verified

The final (a) pressure is 1.1368 atm and (b) temperature is 321 K.

Step by step solution

Preparing the bases of the formulas

(a) This is an adiabic process. So, it can be wriiten that

$p_{1} {V_{1}}^{γ} = p_{2} {V_{2}}^{γ} \frac{p_{2}}{p_{1}} = {(\frac{V_{1}}{V_{2}})}^{γ} p_{2} = p_{1} {(\frac{V_{1}}{V_{2}})}^{γ} \dots \dots \dots \dots \dots \dots (1)$

(b) The number of moles remains constant. From the ideal gas law,

$\frac{p_{1} V_{1}}{T_{1}} = \frac{p_{2} V_{2}}{T_{2}} T_{2} = \frac{p_{2}}{p_{1}} \frac{V_{2}}{V_{1}} T_{1}$

and from part (a),

$\frac{p_{2}}{p_{1}} = {(\frac{V_{1}}{V_{2}})}^{γ}$

Substitutiong this equation, it can be continue finding,

$T_{2} = {(\frac{V_{1}}{V_{2}})}^{γ} \frac{V_{2}}{V_{1}} T_{1} = {(\frac{V_{1}}{V_{2}})}^{γ - 1} T_{1} \dots \dots \dots \dots (2)$

Putting the values

(a) $O_{2}$ is a diatomic gas.

So, $γ = 1.40$ , Substituting this and the volume ratio, it can find from the equation (1) ,

$p_{2} = 3 \cdot 0 . 5^{1.40} = 1.1368 a t m$

(b) By putting the numerical values on the equation (2),

$T_{2} = 0 . 5^{1.40 - 1} \cdot 423 = 321 K$

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.

A gas cylinder holds 0.10 mol of O2 at 150 $°$ C and a pressure
of 3.0 atm. The gas expands adiabatically until the volume is doubled.
What are the final (a) pressure and (b) temperature?

Short Answer

Step by step solution

Preparing the bases of the formulas

Putting the values

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Rotational Dynamics

Classical Mechanics

Electricity and Magnetism

Magnetism

Radiation

Quantum Physics

Study anywhere. Anytime. Across all devices.

A gas cylinder holds 0.10 mol of O2 at 150°C and a pressureof 3.0 atm. The gas expands adiabatically until the volume is doubled.What are the final (a) pressure and (b) temperature?

Short Answer

Step by step solution

Preparing the bases of the formulas

Putting the values

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Rotational Dynamics

Classical Mechanics

Electricity and Magnetism

Magnetism

Radiation

Quantum Physics

Study anywhere. Anytime. Across all devices.

A gas cylinder holds 0.10 mol of O2 at 150 $°$ C and a pressure
of 3.0 atm. The gas expands adiabatically until the volume is doubled.
What are the final (a) pressure and (b) temperature?