# Calculating final pressure and temperature of cylinder

• mh1985
In summary, the conversation discusses the process of calculating the final pressure and temperature when a cylinder is rapidly compressed with a compression ratio of 15, using a value of n = 1.1. The equation for adiabatic compression is used, along with the ideal gas equation, to form an equation involving only pressure and temperature. Through substitution and simplification, the final temperature is determined to be 381.171 K.
mh1985

## Homework Statement

Using a value of n of 1.1, calculate the final pressure and temperature when the cylinder is compressed rapidly with a compression ratio of 15.

Starting pressure = 101.325 kPa
Starting temp = 298 K

(V2/V1) = 15

## The Attempt at a Solution

Rapid compression would mean that the compression is adiabatic. So you also know what other equation?

The compression ratio would be P2/P1=15 and you know what P1 is.

Using the above equation you found and the ideal gas equation, can you form an equation involving only P and T?

rock.freak667 said:
Rapid compression would mean that the compression is adiabatic. So you also know what other equation?

The compression ratio would be P2/P1=15 and you know what P1 is.

Using the above equation you found and the ideal gas equation, can you form an equation involving only P and T?

Thanks for the reply,

So I multiply both sides of P2/P1=15 by P1 to get P2,

101325 * 15 = P2 = 1519875 Pa

Not sure how to form the equation involving only P & T...

Something like T2/T1 = (P2/P1)^((n-1)/n)

EDIT:

so (P2/P1)^((n-1)/n) = 15^(1.1 - 1)/1.1 = 1.2791

1.2791 = T2/T1

T1*1.2791 = T2 = 381.171 K

Not sure if this is right?

Last edited:
mh1985 said:
Thanks for the reply,

So I multiply both sides of P2/P1=15 by P1 to get P2,

101325 * 15 = P2 = 1519875 Pa

Not sure how to form the equation involving only P & T...

Something like T2/T1 = (P2/P1)^((n-1)/n)

EDIT:

so (P2/P1)^((n-1)/n) = 15^(1.1 - 1)/1.1 = 1.2791

1.2791 = T2/T1

T1*1.2791 = T2 = 381.171 K

Not sure if this is right?

Well you'd have P1Vn1=P2V22 and P1V1/T1 = P2V2/T2

Take the last equation, make V1 the subject and substitute it into the first,the V2 should at least cancel out if I remember correctly.

rock.freak667 said:
Well you'd have P1Vn1=P2V22 and P1V1/T1 = P2V2/T2

Take the last equation, make V1 the subject and substitute it into the first,the V2 should at least cancel out if I remember correctly.

Hi thanks for the reply

If I make V1 the subject, I get P2V2T1 /P1T2, right so far? :S

But I don't see how to substitute it into the first equation?

P1 * (P2V2T1 /P1T2) = P2V2^2

mh1985 said:
Hi thanks for the reply

If I make V1 the subject, I get P2V2T1 /P1T2, right so far? :S

But I don't see how to substitute it into the first equation?

P1 * (P2V2T1 /P1T2) = P2V2^2

Sorry, I meant your equation to sub into should be

P1V1n=P2V2n

Just sub your first equation and the volume should cancel out.

rock.freak667 said:
Sorry, I meant your equation to sub into should be

P1V1n=P2V2n

Just sub your first equation and the volume should cancel out.

So I have:

P1* (P2T1/P1T2)n= V2 ?

mh1985 said:
So I have:

P1* (P2T1/P1T2)n= V2 ?

You have

$$V_1= \frac{P_2 V_2 T_1}{T_2 P_1}$$

and

$$P_1V_1^n = P_2V_2^n$$

so that

$$P_1 \left( \frac{P_2 V_2 T_1}{T_2 P_1} \right)^n = P_2V_2^n$$

You can see that V2n is common to both sides and it will cancel out leaving you with only pressure and temperature variables. Thus you can easily get T2 with some simple algebra.

## 1. How do I calculate the final pressure and temperature of a cylinder?

In order to calculate the final pressure and temperature of a cylinder, you will need to know the initial pressure and temperature, as well as the volume and the type of gas inside the cylinder. You will also need to use the ideal gas law, which states that pressure and temperature are directly proportional to each other.

## 2. What is the ideal gas law?

The ideal gas law is a formula that relates the pressure, volume, temperature, and number of moles of an ideal gas. It is written as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

## 3. How do I convert units when calculating final pressure and temperature?

When using the ideal gas law, it is important to make sure that all units are consistent. If you are using SI units, you will need to convert pressure from atmospheres to pascals, and temperature from degrees Celsius to kelvins. If you are using imperial units, you will need to convert pressure from pounds per square inch to atmospheres, and temperature from degrees Fahrenheit to degrees Rankine.

## 4. Can I use the ideal gas law for any gas?

The ideal gas law is most accurate for ideal gases, which are gases that follow the ideal gas law at all temperatures and pressures. However, it can also be used for real gases that behave similarly to ideal gases at certain temperatures and pressures.

## 5. Are there any other factors I should consider when calculating final pressure and temperature of a cylinder?

In addition to the ideal gas law, other factors that may affect the final pressure and temperature of a cylinder include external factors such as changes in atmospheric pressure and temperature, and internal factors such as leaks or changes in volume due to compression or expansion. It is important to consider these factors and make necessary adjustments to your calculations for accuracy.

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