Math / Data & Statistics

QuestionThe data represents a sample of gas that has a constant volume and number of particles. Use the data to answer these two questions.
When the Kelvin temperature of the gas is tripled (increased by a factor of three), the pressure of the gas becomes $\qquad$ \begin{tabular}{|c|c|c|} \hline Trial & \begin{tabular}{c} Temperature \\ $\mathbf{( K )}$ \end{tabular} & \begin{tabular}{c} Pressur \\ (atm) \end{tabular} \\ \hline 1 & 200 & 0.80 \\ \hline 2 & 300 & 1.20 \\ \hline 3 & 400 & 1.60 \\ \hline 4 & 600 & 2.40 \\ \hline 5 & 800 & 3.20 \\ \hline \end{tabular} three times larger Displaying option 3 of 7.
Which set of trials demonstrate this relationship? Select all that apply. Rows 1 and 2 Rows 2 and 4 Rows 1 and 3 Rows 1 and 4 Rows 2 and 5 Rows 1 and 5 Rows 3 and 4

Studdy Solution

STEP 1

What is this asking? If we triple the temperature of some gas (keeping other stuff constant), does the pressure triple too?
Which rows in the table show this tripling effect? Watch out! Make sure you're looking at the temperature in Kelvin, not Celsius or Fahrenheit!
Also, be super careful to compare the right rows.

STEP 2

1. Find the Pressure-Temperature Relationship
2. Check for Tripling

STEP 3

Let's see what happens to the pressure when we triple the temperature!
We're given a table of temperatures and pressures.
We need to find pairs of trials where one temperature is triple the other.

STEP 4

Let's look at Trial 1.
The temperature is $200$ K.
Tripling that gives us $3 \cdot 200 = 600$ K.
Hey, that's the temperature in Trial 4!

STEP 5

Now, let's check the pressures.
In Trial 1, the pressure is $0.80$ atm.
Tripling that gives us $3 \cdot 0.80 = 2.40$ atm.
Wow, that's exactly the pressure in Trial 4!

STEP 6

So, when we triple the temperature from $200$ K to $600$ K, the pressure also triples from $0.80$ atm to $2.40$ atm.
That's cool!
This tells us that Rows 1 and 4 demonstrate the relationship.

STEP 7

Let's see if any other pairs of trials show this tripling effect.
We're looking for a trial where the temperature is three times another trial's temperature, and the pressure is also three times larger.

STEP 8

Look at Trial 1 again, with a temperature of $200$ K.
If we triple this, we get $600$ K.
Is there a trial with this temperature?
Yes, Trial 4!

STEP 9

Now, let's check the pressures for Trials 1 and 4.
Trial 1 has a pressure of $0.80$ atm.
Trial 4 has a pressure of $2.40$ atm.
Is $2.40$ three times $0.80$ ?
You bet! $3 \cdot 0.80 = 2.40$ .

STEP 10

Let's check another pair.
If we triple the temperature of Trial 2 ( $300$ K), we get $3 \cdot 300 = 900$ K.
Oops, there's no trial with $900$ K.

STEP 11

What about tripling Trial 3's temperature ( $400$ K)?
We get $3 \cdot 400 = 1200$ K.
Nope, no $1200$ K trial either.

STEP 12

Rows 1 and 4 demonstrate the relationship where tripling the temperature triples the pressure.

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Studdy Solution

STEP 1

STEP 2

1. Find the Pressure-Temperature Relationship
2. Check for Tripling

STEP 3

Let's see what happens to the pressure when we triple the temperature!
We're given a table of temperatures and pressures.
We need to find pairs of trials where one temperature is triple the other.

STEP 4

Let's look at Trial 1.
The temperature is $200$ K.
Tripling that gives us $3 \cdot 200 = 600$ K.
Hey, that's the temperature in Trial 4!

STEP 5

Now, let's check the pressures.
In Trial 1, the pressure is $0.80$ atm.
Tripling that gives us $3 \cdot 0.80 = 2.40$ atm.
Wow, that's exactly the pressure in Trial 4!

STEP 6

So, when we triple the temperature from $200$ K to $600$ K, the pressure also triples from $0.80$ atm to $2.40$ atm.
That's cool!
This tells us that Rows 1 and 4 demonstrate the relationship.

STEP 7

Let's see if any other pairs of trials show this tripling effect.
We're looking for a trial where the temperature is three times another trial's temperature, and the pressure is also three times larger.

STEP 8

Look at Trial 1 again, with a temperature of $200$ K.
If we triple this, we get $600$ K.
Is there a trial with this temperature?
Yes, Trial 4!

STEP 9

Now, let's check the pressures for Trials 1 and 4.
Trial 1 has a pressure of $0.80$ atm.
Trial 4 has a pressure of $2.40$ atm.
Is $2.40$ three times $0.80$ ?
You bet! $3 \cdot 0.80 = 2.40$ .

STEP 10

Let's check another pair.
If we triple the temperature of Trial 2 ( $300$ K), we get $3 \cdot 300 = 900$ K.
Oops, there's no trial with $900$ K.

STEP 11

What about tripling Trial 3's temperature ( $400$ K)?
We get $3 \cdot 400 = 1200$ K.
Nope, no $1200$ K trial either.

STEP 12

Rows 1 and 4 demonstrate the relationship where tripling the temperature triples the pressure.

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Studdy Solution

STEP 1

STEP 2

1. Find the Pressure-Temperature Relationship2. Check for Tripling

STEP 3

Let's see what happens to the pressure when we triple the temperature!We're given a table of temperatures and pressures.We need to find pairs of trials where one temperature is triple the other.

STEP 4

Let's look at Trial 1.The temperature is 200200200 K.Tripling that gives us 3⋅200=6003 \cdot 200 = 6003⋅200=600 K.Hey, that's the temperature in Trial 4!

STEP 5

Now, let's check the pressures.In Trial 1, the pressure is 0.800.800.80 atm.Tripling that gives us 3⋅0.80=2.403 \cdot 0.80 = 2.403⋅0.80=2.40 atm.Wow, that's exactly the pressure in Trial 4!

STEP 6

So, when we triple the temperature from 200200200 K to 600600600 K, the pressure also triples from 0.800.800.80 atm to 2.402.402.40 atm.That's cool!This tells us that Rows 1 and 4 demonstrate the relationship.

STEP 7

Let's see if any other pairs of trials show this tripling effect.We're looking for a trial where the temperature is three times another trial's temperature, and the pressure is also three times larger.

STEP 8

Look at Trial 1 again, with a temperature of 200200200 K.If we triple this, we get 600600600 K.Is there a trial with this temperature?Yes, Trial 4!

STEP 9

Now, let's check the pressures for Trials 1 and 4.Trial 1 has a pressure of 0.800.800.80 atm.Trial 4 has a pressure of 2.402.402.40 atm.Is 2.402.402.40 three times 0.800.800.80?You bet! 3⋅0.80=2.403 \cdot 0.80 = 2.403⋅0.80=2.40.

STEP 10

Let's check another pair.If we triple the temperature of Trial 2 (300300300 K), we get 3⋅300=9003 \cdot 300 = 9003⋅300=900 K.Oops, there's no trial with 900900900 K.

STEP 11

What about tripling Trial 3's temperature (400400400 K)?We get 3⋅400=12003 \cdot 400 = 12003⋅400=1200 K.Nope, no 120012001200 K trial either.

STEP 12

Rows 1 and 4 demonstrate the relationship where tripling the temperature triples the pressure.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Find the Pressure-Temperature Relationship
2. Check for Tripling

Let's see what happens to the pressure when we triple the temperature!
We're given a table of temperatures and pressures.
We need to find pairs of trials where one temperature is triple the other.

Let's look at Trial 1.
The temperature is $200$ K.
Tripling that gives us $3 \cdot 200 = 600$ K.
Hey, that's the temperature in Trial 4!

Now, let's check the pressures.
In Trial 1, the pressure is $0.80$ atm.
Tripling that gives us $3 \cdot 0.80 = 2.40$ atm.
Wow, that's exactly the pressure in Trial 4!

So, when we triple the temperature from $200$ K to $600$ K, the pressure also triples from $0.80$ atm to $2.40$ atm.
That's cool!
This tells us that Rows 1 and 4 demonstrate the relationship.

Let's see if any other pairs of trials show this tripling effect.
We're looking for a trial where the temperature is three times another trial's temperature, and the pressure is also three times larger.

Look at Trial 1 again, with a temperature of $200$ K.
If we triple this, we get $600$ K.
Is there a trial with this temperature?
Yes, Trial 4!

Now, let's check the pressures for Trials 1 and 4.
Trial 1 has a pressure of $0.80$ atm.
Trial 4 has a pressure of $2.40$ atm.
Is $2.40$ three times $0.80$ ?
You bet! $3 \cdot 0.80 = 2.40$ .

Let's check another pair.
If we triple the temperature of Trial 2 ( $300$ K), we get $3 \cdot 300 = 900$ K.
Oops, there's no trial with $900$ K.

What about tripling Trial 3's temperature ( $400$ K)?
We get $3 \cdot 400 = 1200$ K.
Nope, no $1200$ K trial either.