CHEM 123 Lecture 14: Half-life of 1st & 2nd order reactions

Consider the stretching of a rubber band. Let l, be the length of the unstretched rubber band and I be the length of the stretched rubber band such that -, is the length of the stretching One may write dw = +Fdl which reflects the convention that stretching does work to the system and is positive. Thus, one gets dU = dq + dw = TdS + Fall . The Legendre transformation gives A-U -TS Show that -(a) dA=F41-ST , (b) (a)T 01) =-s , and Or as (d) In class I described an empirical finding. Based upon that information, indicate thesignofG.. Destheentropy increase ordecrease withstretchinga constant temperature? Offer a molecular interpretation for this behavior. (e) Develop an expression for 1-1 in terms of F, T, and l.

Consider the stretching of a rubber band. Let l, be the length of the unstretched rubber band and 11 be the length of the stretched rubber band such that l = 11-4 is the length of the stretching. One may write which reflects the convention that stretching does work to the system and is positive. Thus, one gets dU = dq + dw = TdS + Fal . The Legendre transformation gives A=U-TS Show that -(a) dA=Fdl-SdT , aA-s, and OT) (b) (aA | as) al (c) OT (d) In class I described an empirical finding. Based upon that information, indicate the sign of! constant temperature? Offer a molecular interpretation for this behavior. Does the entropy increase or decrease with stretching at au )Developan expressionforぼ), intermsofF, T,andl.