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.).
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.).