Physical conditions of molecular gas in the first quadrant of the Galaxy are examined through comparison of the CO J = 2-1 data of the Tokyo-Nobeyama Radio Observatory survey with the CO J = 1-0 data of the Columbia survey. A gradient of the CO J = 2-1/J = 1-0 intensity ratio (≡ R2-1/1-0) with Galactocentric distance is reported. The ratio varies from 0.75 at 4 kpc to 0.6 at 8 kpc in Galactocentric distance. This confirms the early in-plane results reported by Handa et al. We classify molecular gas into three categories in terms of R2-1/1-0 on the basis of a large velocity gradient model calculation. Very high ratio gas (VHRG; R2-1/1-0 > 1.0) is either dense, warm, and optically thin gas or externally heated, dense gas. High ratio gas (HRG; R2-1/1-0 = 0.7-1.0) is warm and dense gas with high-excitation temperature of the J = 2-1 transition (Tex 10 K), and it is often observed in central regions of giant molecular clouds. Low ratio gas (LRG; R2-1/1-0 < 0.7) has low-excitation temperature of the J = 2-1 transition (Tex 10 K) because of low density or low kinetic temperature, or both, and is often observed in dark clouds and outer envelopes of giant molecular clouds. It is shown that the CO J = 2-1 emission is better characterized as a tracer of dense gas rather than a tracer of warm gas for molecular gas with kinetic temperature higher than 10 K. The observed large-scale decrease in R2-1/1-0 as a function of Galactocentric distance is ascribed to the fractional decrease of HRG and VHRG from 40% near 5 kpc to 20% near the solar circle. The HRG and VHRG are found predominantly along the Sagittarius and Scutum arms, probably in their downstream. This fact and the deficiency of atomic gas compared with molecular gas in the inner Galaxy indicate that physical conditions of interstellar gas are affected by grand-design, nonlinear processes, such as compression by spiral density waves followed by gravitational collapse, and not by dissociation of low-density molecular gas by young stars.