Calculate the mass of the air in the cylinder

In summary, a vertical cylinder with a heavy piston contains air at a temperature of 300 K, initial pressure of 250 kPa, and initial volume of 0.350 m^3. The molar mass of air is 28.9 g/mol and CV = 5R / 2. To calculate the mass of air in the cylinder, use PV = nRT to find the number of moles. For the energy input required to raise the temperature to 700 K when the piston is held fixed, use Q = (5/2) * nR * delta T. When the piston is free to move, use Q = (5/2) * nR * delta T + W to find the energy
  • #1
lunarskull
28
0
A vertical cylinder with a heavy piston contains air at a temperature of 300 K. The initial pressure is 250 kPa and the initial volume is 0.350 m^3. Take the molar mass of air as 28.9 g/mol and assume that CV = 5R / 2.
(b) Calculate the mass of the air in the cylinder.
I know I have to use the volume that they provided me and the molar mass of air to somehow calculate the mass of the air in cylinder. Could someone please give me a hint in the right direction?
 
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  • #2
lunarskull said:
Take the molar mass of air as 28.9 g/mol and assume that CV = 5R / 2.

(b) Calculate the mass of the air in the cylinder.

Do you have sufficient information to find the number of moles, n, in the cylinder?
 
  • #3
dynamicsolo said:
Do you have sufficient information to find the number of moles, n, in the cylinder?

I am not sure I do, maybe I could figure out how many moles are in 1 liter? Otherwise, I suppose I could calculate the specific heat into kj/kg*K to get the kg units, but I am not sure that would help all that much.
 
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  • #4
lunarskull said:
I am not sure I do, maybe I could figure out how many moles are in 1 liter? Otherwise, I suppose I could calculate the specific heat into kj/kg*K to get the kg units, but I am not sure that would help all that much.

Won't n = PV/RT?

What are the other parts of this problem?
 
  • #5
dynamicsolo said:
Won't n = PV/RT?

What are the other parts of this problem?

Thanks a lot for the help, i figured out the answer to part b of this question along with parts (a) and (c). I am stuck on part (d) now though...

The questions and answers to the respective problems are listed below:


(a) Find the specific heat of air at constant volume in units of kJ/kg·K.

.71 kg/ j*K

(b) Calculate the mass of the air in the cylinder.

(c) Suppose the piston is held fixed. Find the energy input required to raise the temperature of the air to 700 K.

291.7 J

(d) Assume again the conditions of the initial state and that the heavy piston is free to move. Find the energy input required to raise the temperature to 700 K.

I would use n* deltaT * 5R/2 to calculate this, but I am not sure how to calculate how much more energy I would need if the "heavy" piston is free to move.
 
  • #6
lunarskull said:
(c) Suppose the piston is held fixed. Find the energy input required to raise the temperature of the air to 700 K.

291.7 J

(d) Assume again the conditions of the initial state and that the heavy piston is free to move. Find the energy input required to raise the temperature to 700 K.

I would use n* deltaT * 5R/2 to calculate this, but I am not sure how to calculate how much more energy I would need if the "heavy" piston is free to move.

That's what you'd use for part (c) also. Since it's a constant volume process, Q = delta-U = (5/2) · nR · delta T. What did you find for n?

For part (d), letting the piston move freely means that the force applied by the gas pressure balances the weight of the piston. In other words, this is a constant-pressure process. While delta-U is again (5/2) · nR · delta T, you now need to find the work done in this process with the volume going to its new value (which must also be found) in order to determine the heat input.
 
  • #7
dynamicsolo said:
That's what you'd use for part (c) also. Since it's a constant volume process, Q = delta-U = (5/2) · nR · delta T. What did you find for n?

For part (d), letting the piston move freely means that the force applied by the gas pressure balances the weight of the piston. In other words, this is a constant-pressure process. While delta-U is again (5/2) · nR · delta T, you now need to find the work done in this process with the volume going to its new value (which must also be found) in order to determine the heat input.

n came out to be 35.098 mol which i multiplied by .0289 kg/mol to get the mass in kg. How would i calculate the new volume though?
 
  • #8
lunarskull said:
A vertical cylinder with a heavy piston contains air at a temperature of 300 K. The initial pressure is 250 kPa and the initial volume is 0.350 m^3.

(d) Assume again the conditions of the initial state and that the heavy piston is free to move. Find the energy input required to raise the temperature to 700 K.

How would i calculate the new volume though?

You know the pressure remains at 250 kPa and you have the number of moles and the new temperature. So V' = nRT'/P .

BTW, while I agree with your result for n, I rather think that the answer to part (c) is somewhat more than 292 J...

[EDIT: This wouldn't happen to be Problem 17.33 in Serway & Jewett, would it? I just spotted it in the book when I met some of my students today...]
 
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1. How do you calculate the mass of air in a cylinder?

To calculate the mass of air in a cylinder, you need to know the volume of the cylinder and the density of air. The formula for calculating mass is mass = density x volume. The density of air can vary depending on factors such as temperature and pressure, so it is important to use the correct value for your specific situation. Once you have the values for density and volume, you can plug them into the formula to calculate the mass of air in the cylinder.

2. What is the density of air?

The density of air is the amount of mass per unit volume of air. It is typically measured in kilograms per cubic meter (kg/m^3). The density of air can vary depending on factors such as altitude, temperature, and humidity. At sea level and room temperature, the density of air is approximately 1.2 kg/m^3.

3. How does air pressure affect the mass of air in a cylinder?

Air pressure does not directly affect the mass of air in a cylinder. However, changes in air pressure can affect the density of air, which in turn can affect the mass. As air pressure increases, the density of air also increases, resulting in a higher mass of air in the cylinder. Similarly, as air pressure decreases, the density of air decreases, resulting in a lower mass of air in the cylinder.

4. Can the mass of air in a cylinder change?

Yes, the mass of air in a cylinder can change. This can happen due to factors such as changes in air pressure, temperature, and humidity. Additionally, if air is added or removed from the cylinder, the mass of air will also change.

5. How is the mass of air in a cylinder used in scientific experiments?

The mass of air in a cylinder is an important measurement in many scientific experiments. It can be used to calculate the amount of air needed for a specific reaction or to determine the density of other substances. It is also used in calculations for gas laws, such as the ideal gas law. By accurately measuring the mass of air in a cylinder, scientists can better understand and predict the behavior of gases in various conditions.

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