(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
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
To solve these questions, we need to understand the concepts and formulas related to temperature, resistance, temperature coefficient of resistance, and kinetic energy.
(Q1) To find the resistance of the lamp at room temperature (20°C), we can use the formula for resistance:
Resistance = Voltage^2 / Power
Given:
Voltage (V) = 12V
Power (P) = 36W
First, let's find the current (I) using Ohm's Law:
Current (I) = Power / Voltage = 36W / 12V = 3A
To find the resistance at the operating temperature, we need to find the resistance at room temperature and then apply the temperature coefficient of resistance.
Now, let's calculate the resistance at room temperature (20°C):
Given:
Temperature (T1) = 20°C
Temperature (T2) = 1730°C
Temperature Coefficient of Resistance (α) = 0.006/K
Resistance at Room Temperature (R1) = ?
Resistance at Operating Temperature (R2) = ?
To find R1, we can use the temperature relationship formula for resistance:
R1 = R2 / (1 + α*(T2 - T1))
Substituting the values:
R1 = R2 / (1 + 0.006*(1730 - 20))
R1 = R2 / (1 + 0.006*1710)
R1 = R2 / (1 + 10.26)
R1 = R2 / 11.26
Now, we know that the resistance at operating temperature (R2) is related to the power and current as follows:
R2 = Voltage^2 / Power = 12V^2 / 36W = 4Ω
Substituting the value of R2 in the equation for R1:
R1 = 4Ω / 11.26
R1 ≈ 0.3548Ω
Therefore, the resistance of the lamp at room temperature (20°C) is approximately 0.3548Ω.
Comparing the options given, none of them match the calculated value of 0.3548Ω. Please double-check the options or calculations.
(Q2) To find the temperature at which the root-mean-square speed of oxygen molecules is 640m/s, we can use the formula for root-mean-square speed:
v = √(3kT / m)
Given:
Root-Mean-Square Speed (v) = 640m/s
Mass of oxygen (m) = 32kg (1 kilomole)
To find T (Temperature), we need to rearrange the formula:
T = (v^2 * m) / (3k)
Now, we need the value of Boltzmann's constant (k), which is approximately 1.38 x 10^-23 J/K.
Substituting the values in the formula:
T = (640^2 * 32) / (3 * 1.38 x 10^-23)
Calculating further:
T = (409600 * 32) / (4.14 x 10^-23)
T ≈ 251,223,574,850,299,401,197,604.65 K
Converting it to Celsius, we subtract 273.15 K:
T ≈ 251,223,574,850,299,400,924,339.5°C
Rounding it to the nearest whole number, we get:
T ≈ 251,223,574,850,299,400,924,340°C
Therefore, the temperature at which the root-mean-square speed of oxygen molecules is 640m/s is approximately 251,223,574,850,299,400,924,340°C.
Among the options given, none of them match the calculated value. Please double-check the options or calculations.
(Q3) To calculate the average translational kinetic energy of a nitrogen molecule at 27°C, we can use the formula:
Kinetic Energy (KE) = (3/2) * k * T
Given:
Temperature (T) = 27°C = 27 + 273.15 K (converting to Kelvin)
Boltzmann's constant (k) is approximately 1.38 x 10^-23 J/K.
Substituting the values in the formula:
KE = (3/2) * 1.38 x 10^-23 J/K * (27 + 273.15) K
Calculating further:
KE ≈ (3/2) * 1.38 x 10^-23 J/K * 300.15 K
KE ≈ 2.07 x 10^-23 J
Therefore, the average translational kinetic energy of a nitrogen molecule at 27°C is approximately 2.07 x 10^-23 J.
Comparing the options given, the closest match is (d) 0.00000000421. Please note that there might be rounding or conversion differences in the options.