Question

(Q1)the temperature at which the tungsten filament of a 12v and 36w lamp operates is 1730c.If the temperature coefficient of resistance of tungsten is 0.006/k, find the resistance of the lamp at room temperature of 20c (a)10.00(b)0.45ohms(c)0.39ohms(d)4.00ohms (Q2)At what temperature will the root-mean-square speed of oxygen molecules have the value of 640m/s?1 kilomole of oxygen has a mass of 32kg.(a)252.5(b)332.3(c)272.2(d)373.2 (Q3)calculate the average translational kinetic energy of a nitrogen molecule at 27c (a)0.0000000000621 (b)0.000000073(b)0.00000000542(d)0.00000000421

Answer 1

Q1
R is the resistance at 1730℃
P=U²/R = >
R=U²/P = 12²/36= 4 Ohms
ΔR/R₀=αΔ T
(R-R₀)/R₀=αΔ T
Δ T=T-T₀=1730-0 =1730
R- R₀=R₀•α•Δ T
R₀=R/(1+ α•Δ T) = 0.351 Ohms
R₁ ia the resistance at 20℃
R₁=R₀{1+ αΔT₁} = 0.351•{1+0.006•20} = 0.393 Ohms

Q2
v = sqrt{3RT/M} =>
T= v²M/3R = 640²•32•10⁻³/3•8.31 = 525.7 K
T(℃) =525.7 – 273.15 = 252.55 ℃

Q3
E=ikT/2 =3kT/2 = 3•1.38•10⁻²³•300/2 =6.21•10⁻²¹ J