Gas laws

[Emilooo]

Hey everyone. I would really appreciate some help with the following maths problem. My inkling is that it should be basic laws of logarithms, but I just don’t know where to start. Thanks in advance for the help.


a) The pressure, ?, and volume, ?, of a gas are related by ln ? = −? ln ? + ln ?
where ? and ? are constants. Show that, ln??? =ln?


b) A gas in a cylinder has an initial volume of 0.01 ?3 at a pressure of 250 ???−2. The gas
is then compressed by a piston to a pressure of 800 ???−2 according to the law
? ?1.2 = ? ?1.2 11 22
Using EITHER the laws of indices OR logarithms, find the new volume of the gas and state your answer in standard form to three significant figures (3 s.f.).

 

[Dr.Peterson]

a) The pressure, ?, and volume, ?, of a gas are related by ln ? = −? ln ? + ln ?
where ? and ? are constants. Show that, ln??^? =ln?

Yes, you just need to apply the laws of logs. Please show what you found when you tried that.

Please observe that you can simplify further than ln(PVⁿ) = ln(C). Using the more simplified form will help in part (b).

b) A gas in a cylinder has an initial volume of 0.01 ?3 at a pressure of 250 ???−2. The gas
is then compressed by a piston to a pressure of 800 ???−2 according to the law
? ?1.2 = ? ?1.2 11 22

Pasting seems to have messed this up. Please either proofread and correct it, or give us an image of the original.

The method for this part will be much like many problems you should have seen before, such as proportions or "variation". Take the given case and calculate the constant C, then use that to find the volume in the second case.

 

[Emilooo]

Hi, thank you for your reply. I have attached a photo of the question. Pasting did mess up the question. Thanks again.

 

[Dr.Peterson]

Hi, thank you for your reply. I have attached a photo of the question. Pasting did mess up the question. Thanks again.

Thanks.

Now we need to see some work, in order to know what help you need beyond my suggestions.