# Gases & Pressure: Solving Homework Equations

• parwana
In summary: SI unit, and has a different base unit than Kelvin)In summary, an expandable cylinder with a top connected to a spring with force constant 2.00 x 10^3 N/m is filled with 4.00 L of gas at a pressure of 1.00 atm and a temperature of 20.0 °C. The lid has a cross-sectional area of 0.0100 m^2 and negligible mass. The problem is to find the height the lid will rise when the temperature is raised to 230 °C and the pressure of the gas at 230 °C. Using the equations PV=nRT and PiVi/Ti=PfVf/Tf,
parwana

## Homework Statement

An expandable cylinder has its top connected to a spring with force constant 2.00 103 N/m. (See Fig. P10.58.) The cylinder is filled with 4.00 L of gas with the spring relaxed at a pressure of 1.00 atm and a temperature of 20.0°C.

(a) If the lid has a cross-sectional area of 0.0100 m2 and negligible mass, how high will the lid rise when the temperature is raised to T = 230°C?

(b) What is the pressure of the gas at 230°C?

PV=nRT
PiVi/Ti= PfVf/Tf

## The Attempt at a Solution

Ok I did Pf= Pinitial+ k(spring constant)(h)/Area
Also Vf= Vi + h(Area)

Then I plugged these into the PiVi/Ti= PfVf/Tf
and its not the right answer

What am I doing wrong?

Looks reasonable at first glance. Can you show your math with units so we can check?

((1.013X10^5 Pascals)(.004m^3))/20 Celsius= (((1.013X10^5 Pascals + 2X10^3N/m X height)/0.0100 meters^2)(.004m^3 + 0.0100meters^2 X height))/all over 230 Celsius

Last edited:
I guess I was looking for a more step-by step development, but whatever. Where is the 1atm of initial pressure again? What units are you using? Be sure to include *all* units to be sure that they are consistent.

the 1 atm of pressure= 1.013X10^5 Pascals

I edited it to include the units

Are Pascals, ml, N and m all compatible units? What are the base units of Pascals? (Sorry, I don't know offhand)

It looks like in the first part of the righthand side, you are mixing units of Pascals = N? How can a pressure equal a force? Do you see what I mean about carrying your units along to help you check your equations and manipulations? And near the end there, it looks like you are saying that a ml = m^3?

1 Pa ≡ 1 N/m²

let me convert the ml to m^3, maybe that's the problem

Remember, in order to add terms, they have to have the same base units. And the left and right hand sides of an equation must have the same base units...

I am doing something wrong, I am not getting it right

Re-write the equation, being careful to keep your units consistent as I mentioned in post #8. I have to go now. Good luck.

I don't know what's wrong, its not getting the right answer

can someone help me and try it and see what I am doing wrong and the answer they get?

Units for temperature?

^ I have it there in Celsius

parwana said:
can someone help me and try it and see what I am doing wrong and the answer they get?

Show us the current version of your equation, with the corrected and checked units, and we'll try to help you. We don't do your work for you.

^ I have it written on top but if u want it again

((1.013X10^5 Pascals)(.004m^3))/20 Celsius= (((1.013X10^5 Pascals + 2X10^3N/m X height)/0.0100 meters^2)(.004m^3 + 0.0100meters^2 X height))/all over 230 Celsius

But the units still look wrong to me, which implies that the equation is not formed correctly.

lefthand side --> [ Nm^2/C ]

righthand side --> [ ( ((N/m + N)/m) m^3 )/C ]

hmm I really don't know what I am doing wrong, this is so frustrating

parwana said:
hmm I really don't know what I am doing wrong, this is so frustrating

I think the problem is that you are trying to do too much in one line, and are not being careful about the algebra and units. Try it this way:

What is the answer for PiVi/Ti= ? (show the units of the answer)

Then set that equal to PfVf/Tf (being careful about the algebra and units) and solve for h.

Gokul43201 said:
Units for temperature?

parwana said:
^ I have it there in Celsius

I wasn't asking a question; I was giving you a hint!

Is Celcius the correct unit to describe thermodynamic temperature?

## 1. What is the ideal gas law and how is it used to solve equations?

The ideal gas law is a thermodynamic equation that describes the relationship between the pressure, volume, temperature, and amount of a gas. It is written as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. This equation is used to solve for any of the variables, as long as the other three are known. It is commonly used in chemistry and physics to calculate the properties of gases.

## 2. What is the difference between absolute and gauge pressure?

Absolute pressure is the total pressure exerted by a gas, including atmospheric pressure. It is measured relative to a perfect vacuum. Gauge pressure, on the other hand, is the pressure above atmospheric pressure. It is often used to measure the pressure of a gas in a closed system, such as a tire or a scuba tank.

## 3. How do temperature and pressure affect the volume of a gas?

According to Charles's Law, the volume of a gas is directly proportional to its temperature, as long as the pressure and amount of gas remain constant. This means that as the temperature increases, the volume of the gas will also increase. On the other hand, according to Boyle's Law, the volume of a gas is inversely proportional to its pressure, as long as the temperature and amount of gas remain constant. This means that as the pressure increases, the volume of the gas will decrease.

## 4. How do you convert between units of pressure?

To convert between units of pressure, you can use the following conversions: 1 atm = 101.325 kPa = 760 mmHg = 14.7 psi. Simply multiply or divide by the appropriate conversion factor to convert from one unit to another. It is important to make sure that the units cancel out correctly in the calculation.

## 5. How do you determine the partial pressure of a gas in a mixture?

The partial pressure of a gas in a mixture is the pressure that the gas would exert if it were the only gas present in the container at the same temperature and volume. To determine the partial pressure, you can use Dalton's Law of Partial Pressures, which states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each gas in the mixture. This can be calculated by multiplying the total pressure by the mole fraction of the gas in the mixture.

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