Math / Algebra

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 \begin{tabular}{|c|c|c|} \hline Trial & \begin{tabular}{c} Temperature \\ (K) \end{tabular} & \begin{tabular}{c} Pressure \\ (mm Hg) \end{tabular} \\ \hline 1 & 200 & 400 \\ \hline 2 & 300 & 600 \\ \hline 3 & 400 & 800 \\ \hline 4 & 600 & 1200 \\ \hline 5 & 800 & 1600 \\ \hline \end{tabular} the gas becomes $\qquad$ .

Studdy Solution

STEP 1

What is this asking? If we triple the temperature of some gas (keeping other stuff constant), what happens to the pressure? Watch out! The table gives a bunch of data, but we only need two points to figure out the relationship between temperature and pressure!
Don't get bogged down in extra information.
Also, make sure to use the correct units, which are Kelvin for temperature and mm Hg for pressure.

STEP 2

1. Find the relationship between temperature and pressure.
2. Calculate the new pressure.

STEP 3

Let's look at trials 1 and 2 from our table.
In trial 1, we have a temperature of $T_1 = 200$ K and a pressure of $P_1 = 400$ mm Hg.
In trial 2, we have $T_2 = 300$ K and $P_2 = 600$ mm Hg.
We want to see how the pressure changes when the temperature changes.

STEP 4

Let's check the ratio of the temperatures and pressures between these two trials.
The ratio of temperatures is $\frac{T_2}{T_1} = \frac{300}{200} = \frac{3}{2}$ .
The ratio of pressures is $\frac{P_2}{P_1} = \frac{600}{400} = \frac{3}{2}$ .
Whoa, they're the same!
This tells us that pressure and temperature are directly proportional!

STEP 5

Since the ratios are the same, we can write a proportionality equation: $P = k \cdot T$ , where $k$ is our constant of proportionality.
We can find $k$ using the data from trial 1: $400 = k \cdot 200$ . Dividing both sides by 200 gives us $k = \frac{400}{200} = 2$ .
So, our equation is $P = 2T$ .
This means for every 1 K increase in temperature, the pressure increases by 2 mm Hg.

STEP 6

Let's pick a starting point.
We can use trial 1 again, with $T = 200$ K and $P = 400$ mm Hg.
Now, we're tripling the temperature, so our new temperature is $T_{new} = 3 \cdot 200 = 600$ K.

STEP 7

Using our handy equation $P = 2T$ , we can find the new pressure: $P_{new} = 2 \cdot T_{new} = 2 \cdot 600 = 1200$ mm Hg.
Look at that, the pressure also tripled!
This makes sense because pressure and temperature are directly proportional.

STEP 8

When the Kelvin temperature of the gas is tripled, the pressure becomes 1200 mm Hg.

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Studdy Solution

STEP 1

STEP 2

1. Find the relationship between temperature and pressure.
2. Calculate the new pressure.

STEP 3

Let's look at trials 1 and 2 from our table.
In trial 1, we have a temperature of $T_1 = 200$ K and a pressure of $P_1 = 400$ mm Hg.
In trial 2, we have $T_2 = 300$ K and $P_2 = 600$ mm Hg.
We want to see how the pressure changes when the temperature changes.

STEP 4

STEP 5

STEP 6

Let's pick a starting point.
We can use trial 1 again, with $T = 200$ K and $P = 400$ mm Hg.
Now, we're tripling the temperature, so our new temperature is $T_{new} = 3 \cdot 200 = 600$ K.

STEP 7

Using our handy equation $P = 2T$ , we can find the new pressure: $P_{new} = 2 \cdot T_{new} = 2 \cdot 600 = 1200$ mm Hg.
Look at that, the pressure also tripled!
This makes sense because pressure and temperature are directly proportional.

STEP 8

When the Kelvin temperature of the gas is tripled, the pressure becomes 1200 mm Hg.

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Studdy Solution

STEP 1

STEP 2

1. Find the relationship between temperature and pressure.2. Calculate the new pressure.

STEP 3

STEP 4

STEP 5

STEP 6

Let's pick a **starting point**.We can use trial 1 again, with T=200T = 200T=200 K and P=400P = 400P=400 mm Hg.Now, we're **tripling** the temperature, so our new temperature is Tnew=3⋅200=600T_{new} = 3 \cdot 200 = 600Tnew​=3⋅200=600 K.

STEP 7

STEP 8

When the Kelvin temperature of the gas is tripled, the pressure becomes **1200 mm Hg**.

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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 relationship between temperature and pressure.
2. Calculate the new pressure.

Let's pick a starting point.
We can use trial 1 again, with $T = 200$ K and $P = 400$ mm Hg.
Now, we're tripling the temperature, so our new temperature is $T_{new} = 3 \cdot 200 = 600$ K.

When the Kelvin temperature of the gas is tripled, the pressure becomes 1200 mm Hg.