As a sample of nitrogen gas (N2) undergoes a temperature increase at constant volume, the distribution of molecular speeds increases. That is, the probability distribution function P(v) for the molecules spreads to higher speed values, as suggested in Figure b. One way to report the spread in P(v) is to measure the difference Δv between the most probable speed vp and the rms speed vrms. When P(r) spreads to higher speeds, Ay increases. Assume that the gas is ideal and the N2 molecules rotate but do not oscillate. For 1.5 mol, an initial temperature of 250 K, and a final temperature of 500 K, what are

(a) The initial difference Δvb,

(b) The final difference Δvf, and

(c) The entropy change ΔS for the gas?