Answer:
So a=3.844 and b=5
Explanation:
Scientific notation requests to write a number using powers of ten as a factor accompanying a real number (a) between 1 and smaller than 10 that contains the digits to exactly represent the original number. So in this case, the number 384,400 can be written as:
with a=3.844, and "5" as the exponent of ten (so b=5)
Answer:
(a) 1462.38 m/s
(b) 2068.13 m/s
Explanation:
(a)
The Kinetic energy of the atom can be given as:
K.E = (3/2)KT
where,
K = Boltzman's Constant = 1.38 x 10⁻²³ J/k
K.E = Kinetic Energy of atoms = 343 K
T = absolute temperature of atoms
The K.E is also given as:
K.E = (1/2)mv²
Comparing both equations:
(1/2)mv² = (3/2)KT
v² = 3KT/m
v = √[3KT/m]
where,
m = mass of Helium = (4 A.M.U)(1.66 X 10⁻²⁷ kg/ A.M.U) = 6.64 x 10⁻²⁷ kg
v = RMS Speed of Helium Atoms = ?
Therefore,
v = √[(3)(1.38 x 10⁻²³ J/K)(343 K)/(6.64 x 10⁻²⁷ kg)]
<u>v = 1462.38 m/s</u>
(b)
For double temperature:
T = 2 x 343 K = 686 K
all other data remains same:
v = √[(3)(1.38 x 10⁻²³ J/K)(686 K)/(6.64 x 10⁻²⁷ kg)]
<u>v = 2068.13 m/s</u>
Answer:
Z = R, i = V/Z, w = √1 / LC
Explanation:
In an RLC circuit the impedance of the circuit is
Z = √[R² + (
)²
Where
= wL
X_{L} = 1 / wC
They are the reactances of the inductor and the capacitor, in this case the current advances to the voltage in the first and is delayed from the voltage in the second, so when the two values give the same reactance the current goes in phase with the voltage and the impedance is minimal
Z = R
V= i Z
i = V/Z
Therefore the current is maximum, this occurs when
w = √1 / LC
Saying that this is the resonant frequency
Answer:
a. 960 W b. One 1 kW room heater
Explanation:
a. The rate of heat conduction P = kA(T₂ - T₁)/d where k = 2 × 0.040 W/m-K = 0.080 W/m-K since the thermal conductivity of glass wool is 0.040 W/m-K and that of the material is twice the thermal conductivity of glass wool, A = area of walls = 120 m², T₁ = outside surface temperature = 5.0 °C, T₂ = inside surface temperature = 18.0 °C and d = thickness of wall = 13.0 cm = 0.13 m
P = kA(T₂ - T₁)/d
= 0.080 W/m-K × 120 m²(18.0 °C - 5.0 °C)/0.13 m
= 9.6 Wm/K × 13 K/0.13 m
= 124.8 Wm/0.13 m
= 960 W
b. The number of 1 kW room heater required will be
n = rate of heat conduction/power of one room heater = 960 W/ 1 kW = 960 W/1000 W = 0.96 ≅ 1
So we need only one 1 kW room heater.
