tbr test 3 physical sciences q 40

[2010premed]

---

Members do not see this ad.

To obtain the curve for CO2 that appears in Figure 1, what must be true about the signs of β and γ in Equation 1?
A. Both β and γ must be positive.
B. Both β and γ must be negative.
C. β must be positive, and γ must be negative.
D. β must be negative, and γ must be positive.

How would you go about this question?

 

[PiBond]

the "B" term and gamma term must be opposite signs since the curve is leveling out. if they were the same sign, we'd see a more drastic slope change for CO2 in either direction depending on if they were both positive or negative. therefore, i knock off A and B. now i'm considering what would occur if gamma were positive or negative given that it's multiplied by the T^2 term and will therefore have a more significant effect on my graph. if it were positive and B were negative, the graph wouldn't level out and would curl upwards instead. if it was negative and if the "B" was positive then we'd see if level off like the graph depicts. therefore, I arrive at choice C for my answer

 

[2010premed]

You are right on.

How do you know though that the beta and gamma terms must be opposite signs b/c of the leveling off of the curve? Is this b/c the slop is C/T and since the whole term is getting smaller, then C is getting smaller? In this case, then why not have them both negative?