Discussion

Among the options given, identify the correct match between the polymers and their glass transition temperatures (\(T_{g}\)).

Polymer		Glass transition temperature (°C)
P	High density polyethylene	1	\(\gt 200\)
Q	Poly(vinyl carbazole)	2	145 to 155
R	Polymethyl methacrylate	3	-100 to -80
S	Polycarbonate	4	90 to 100

Answer: B

The correct match is P-3; Q-1; R-4; S-2.

High density polyethylene: a flexible chain with no side groups, so \(T_{g}\) is far below room temperature, around -100 to -80°C (3).
Poly(vinyl carbazole): the very bulky, rigid carbazole side group stiffens the chain enough to push \(T_{g}\) above 200°C (1).
PMMA: an amorphous glassy plastic at room temperature, with \(T_{g}\) usually quoted near 100°C, which is the 90 to 100°C band (4).
Polycarbonate: rigid aromatic rings in the backbone give \(T_{g}\) near 145 to 150°C (2).

The other options misplace these; any option putting HDPE above room temperature, or PMMA above 200°C, can be ruled out at once.

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