Compression and Expansion of a Volume of Air

[Chestermiller]

(b) Inversely proportional to the volume.

So, if the pressure is inversely proportional to the volume and you know the initial and final volumes, and the initial pressure, what is the final volume?

 

[Chestermiller]

I have done some revising and found the equation.

$$T = Q - W$$

This is for Temperature constant.

Am i correct?

No.

 

[Ben_Walker1978]

Is the final pressure 800000 Pa.

I done $$P1V1 = P2V2$$

 

[Chestermiller]

Is the final pressure 800000 Pa.

I done $$P1V1 = P2V2$$

This is not correct. You started Step 2 with a pressure of 14.9 bars, and you increased the volume at constant temperature.

 

[Ben_Walker1978]

The volume at constant temperature was 0.12. So is both the volumes 0.12?

 

[Chestermiller]

The volume at constant temperature was 0.12. So is both the volumes 0.12?

No. During Step 1, the temperature got higher, and it stayed at this value during step 2.

 

[Ben_Walker1978]

Yes the temperature got to 542.99 Kelvin.

But i don't know what equation to use.

 

[Chestermiller]

Yes the temperature got to 542.99 Kelvin.

But i don't know what equation to use.

You already guessed the correct equation to use. in post #13. But, you used the wrong initial pressure, and you applied the equation incorrectly.

 

[Ben_Walker1978]

$$pV^{1.3}=c$$

So change it to
$$P2 = \frac{p1v1^{1.3}}{V2^{1.3}}$$

 

[Chestermiller]

$$pV^{1.3}=c$$

So change it to
$$P2 = \frac{p1v1^{1.3}}{V2^{1.3}}$$

P2=14.9/8=1.86 bars

 

[Ben_Walker1978]

So final pressure is 1.86 bars?

I over complicated the equation for final pressure then.

 

[Ben_Walker1978]

How does this look to you??

i)
Pressure after Compression Ratio =

Volume after compression = $$\frac {Volume}{Compession Ratio} = \frac{0.12}{8} = 0.015$$
Volume after compression = $$0.015m^3$$
$$P1f (V1f)^{1.3} = P1i (V1i)^{1.3}$$
$$P1i = 100000$$
$$V1i = 0.12m^3$$
$$V1f = 0.015m^3$$

$$P1f (0.015)^{1.3} = (100000)(0.12)^{1.3}$$
$$100000 x 0.12^{1.3} = 6352.367569$$
$$6352.367569 / 0.015 = 1492852.786$$
$$P1f = 1492852.786$$
$$(1492852.786)(0.015)^{1.3} = (100000)(0.12)^{1.3}$$

$$Pressure after compression = 1492852.786 Pa$$Temperature after compression=
$$ n = \frac{(100000)(0.12)}{(8.314)(273.2718)} = 4.96 mol$$
$$pV = nRT$$
$$T = \frac{pV}{nR}$$
$$T = \frac{(1492852.786)(0.015)}{(4.96)(8.31441)}$$
$$ 1492852.786 \times 0.015 = 22393.77321$$
$$22393.77321 / 41.239 = 542.99$$
$$ T = 542.99 Kelvin$$

The final pressure =

$$P2 =\frac{Pressure after compression}{Compression Ratio}$$
$$P2 = \frac{14.9}{8} = 1.86 Bar$$

The final pressure = 1.86 Bar

 

[Chestermiller]

Looks good.

 

[Ben_Walker1978]

Good.

Thank you for all your help.

Really appreciate it.

 

[Ben_Walker1978]

I have one more question.

Someone has told me for final pressure you don't divide by compression ratio.

Because i already divided my compression ration.

I have been told final pressure is wrong.

Are they right? Or is it correct?

Thanks.

 

[Chestermiller]

I have one more question.

Someone has told me for final pressure you don't divide by compression ratio.

Because i already divided my compression ration.

I have been told final pressure is wrong.

Are they right? Or is it correct?

Thanks.

The "someone" who told you this is wrong (although you should know that without me having to tell you). The final pressure is correct. In the first step, you compressed the gas, and in the second step, the gas expanded. In the second step, you multiplied the volume from the first step to get you back to the original volume. Who is this "someone?"

 

[Ben_Walker1978]

Thank you for your reply.

Someone who i work with.

So because the gas has expanded then you need to divided it by the compression ratio again?

I was just making sure. As when he said it confused me.

 

[Chestermiller]

Thank you for your reply.

Someone who i work with.

So because the gas has expanded then you need to divided it by the compression ratio again?

I was just making sure. As when he said it confused me.

No. In the first part, you divided the volume by the compression ratio. In the 2nd part, you multiplied the volume by the compression ratio (and divided the pressure by the compression ratio). You are aware that there is a difference between dividing the volume by the compression ratio and dividing the pressure by the compression ratio, right?

 

[Ben_Walker1978]

Yes now i understand.