Calculating final pressure and temperature of cylinder

1. Mar 24, 2012

mh1985

1. The problem statement, all variables and given/known data

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

2. Relevant equations

(V2/V1) = 15

3. The attempt at a solution

2. Mar 25, 2012

rock.freak667

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?

3. Mar 27, 2012

mh1985

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: Mar 27, 2012
4. Mar 27, 2012

rock.freak667

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.

5. Mar 29, 2012

mh1985

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

6. Mar 29, 2012

rock.freak667

Sorry, I meant your equation to sub into should be

P1V1n=P2V2n

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

7. Mar 30, 2012

mh1985

So I have:

P1* (P2T1/P1T2)n= V2 ?

8. Mar 30, 2012

rock.freak667

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.