Question

We have two equal-size boxes, $A$ and $B$. Each box contains gas that behaves as an ideal gas. We insert a thermometer into each box and find that the gas in box $A$ is at 50$^\circ$C while the gas in box $B$ is at 10$^\circ$C. This is all we know about the gas in the boxes. Which of the following statements must be true? Which could be true? Explain your reasoning. (a) The pressure in $A$ is higher than in $B$. (b) There are more molecules in $A$ than in $B$. (c) A and B do not contain the same type of gas. (d) The molecules in $A$ have more average kinetic energy per molecule than those in $B$. (e) The molecules in $A$ are moving faster than those in $B$.

          We have two equal-size boxes, $A$ and $B$. Each box contains gas that behaves as an ideal gas. We insert a thermometer into each box and find that the gas in box $A$ is at 50$^\circ$C while the gas in box $B$ is at 10$^\circ$C. This is all we know about the gas in the boxes. Which of the following statements must be true? Which could be true? Explain your reasoning. (a) The pressure in $A$ is higher than in $B$. (b) There are more molecules in $A$ than in $B$. (c) A and B do not contain the same type of gas. (d) The molecules in $A$ have more average kinetic energy per molecule than those in $B$. (e) The molecules in $A$ are moving faster than those in $B$.

Show more…

Added by Patrick T.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Chapter 18

Instant Answer

Solved by Expert Cyra Jelle Calleja

08/04/2021

Step 1

Step 1: Given that the gas in box A is at 50$^\circ$C and the gas in box B is at 10$^\circ$C, we know that the gas in box A has a higher temperature than the gas in box B. Show more…

Show all steps

lock

Thanks for your feedback!

We have two equal-size boxes, $A$ and $B$. Each box contains gas that behaves as an ideal gas. We insert a thermometer into each box and find that the gas in box $A$ is at 50$^\circ$C while the gas in box $B$ is at 10$^\circ$C. This is all we know about the gas in the boxes. Which of the following statements must be true? Which could be true? Explain your reasoning. (a) The pressure in $A$ is higher than in $B$. (b) There are more molecules in $A$ than in $B$. (c) A and B do not contain the same type of gas. (d) The molecules in $A$ have more average kinetic energy per molecule than those in $B$. (e) The molecules in $A$ are moving faster than those in $B$.

Play audio

Feedback

Powered by NumerAI

Cyra Jelle Calleja and 63 other subject Physics 101 Mechanics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:01 In this problem, we have two boxes of equal volume that both contain an ideal gas.

00:12 The temperature on box a is 50 degrees and the temperature in box b is 10 degrees.

00:23 Now, the problem asks us which of the given statements is true.

00:30 First, for the statement one, the problem states.

00:34 That the pressure on box a or the pressure of gas a is greater than the pressure gas b.

00:43 This is not true or inconclusive because we know from the formula of ideal gas law, pv is equals to nrt.

00:56 So even if v is equal or their volume are equal and the temperature of gas a is greater than gas b, we don't know the number of most in gas a and the number of most in gas b.

01:18 Therefore, either gases or either pressure can be higher than the other.

01:35 Now, for statement b, the problem states that the number of molecules on gas a is greater than the number of molecules in gas b.

01:49 The formula for number of molecules is and is equal.

01:53 To number of moles multiplied by the avogadros constant.

02:01 Again, since we don't know the number of moles, then either gases have molecules greater or lesser than the other.

02:23 Next, for statement c, it states that gas a and gas b are not the same gas.

02:38 They're not the same gas if their molar mass is not equal.

02:44 And we know that a formula for molar mass is the mass of the gas over the number of moles...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later