Final answer:
To maintain the same melt viscosity of 2 x 10^4 poise when the degree of polymerization decreases from 700 to 500, the temperature must be adjusted down. The specifics of the temperature adjustment cannot be determined without an explicit relationship between the variables.
Step-by-step explanation:
The student is essentially asking about the relationship between melt viscosity, degree of polymerization, and temperature. In the context of the polymer described, as the degree of polymerization decreases from 700 to 500, the polymer chains become shorter which affects the melt viscosity. To maintain the same melt viscosity of 2 x 104 poise, the temperature must be adjusted.
While the question does not provide a specific equation or relationship between these variables, we can qualitatively understand the behavior. Shorter chains tend to have lower viscosities as they can slide past each other more easily. Thus, to maintain the same viscosity with shorter chains, one would typically need to decrease the temperature. However, without the explicit relationship or additional data, we cannot definitively calculate the exact temperature needed.