Saladsamurai Messages 3,009 Reaction score 7 Thread starter Oct 24, 2008 #1 I do not understand how they went from [itex]\ln T_c-\lnT_H=\theta_c-\theta_H[/itex] to [itex]\theta=\ln T+C[/itex] Why did the subscripts drop out? What just happened?
I do not understand how they went from [itex]\ln T_c-\lnT_H=\theta_c-\theta_H[/itex] to [itex]\theta=\ln T+C[/itex] Why did the subscripts drop out? What just happened?
physicsnoob93 Messages 169 Reaction score 0 Oct 25, 2008 #2 exp means e^thethac if that is thetha so you get e^(thethac-thethah) is Tc/Th. If you ln both sides, you'll get ln(Tc/Th) = lnTc-lnTh and on the other side lne^(thethac-thethah) = (thethac-thethah)lne. lne is one. Thus lnTc-lnTh = thethac-thethah
exp means e^thethac if that is thetha so you get e^(thethac-thethah) is Tc/Th. If you ln both sides, you'll get ln(Tc/Th) = lnTc-lnTh and on the other side lne^(thethac-thethah) = (thethac-thethah)lne. lne is one. Thus lnTc-lnTh = thethac-thethah
HallsofIvy Science Advisor Homework Helper Messages 42,895 Reaction score 983 Oct 25, 2008 #3 "C" and "H" just represent different measurements of the temperature. Since you take TH to be a fixed temperature, that just leaves one temperature- you don't need the "C" to distinguish it form "H".
"C" and "H" just represent different measurements of the temperature. Since you take TH to be a fixed temperature, that just leaves one temperature- you don't need the "C" to distinguish it form "H".
Saladsamurai Messages 3,009 Reaction score 7 Oct 26, 2008 #4 I am sorry Halls, I don't quite follow. What do you mean I take TH to be fixed?