Answer:
a) 3.39 × 10²³ atoms
b) 6.04 × 10⁻²¹ J
c) 1349.35 m/s
Explanation:
Given:
Diameter of the balloon, d = 29.6 cm = 0.296 m
Temperature, T = 19.0° C = 19 + 273 = 292 K
Pressure, P = 1.00 atm = 1.013 × 10⁵ Pa
Volume of the balloon = 
or
Volume of the balloon = 
or
Volume of the balloon, V = 0.0135 m³
Now,
From the relation,
PV = nRT
where,
n is the number of moles
R is the ideal gas constant = 8.314 kg⋅m²/s²⋅K⋅mol
on substituting the respective values, we get
1.013 × 10⁵ × 0.0135 = n × 8.314 × 292
or
n = 0.563
1 mol = 6.022 × 10²³ atoms
Thus,
0.563 moles will have = 0.563 × 6.022 × 10²³ atoms = 3.39 × 10²³ atoms
b) Average kinetic energy = 
where,
Boltzmann constant, 
Average kinetic energy = 
or
Average kinetic energy = 6.04 × 10⁻²¹ J
c) rms speed = 
where, m is the molar mass of the Helium = 0.004 Kg
or
rms speed = 
or
rms speed = 1349.35 m/s
Answer:
5m/8
Explanation:
Function T gives the time the Hobbits have to prepare for the attack, T(k), in minutes, as a function of troll's distance, k, in meters.
Function V gives visibility from the watchtower, V(m), in meters, as a function of the height of the watchtower, m, in meters.
Therefore, T(V(m)) will give the time the Hobbits have to prepare for the troll attack as a function of the height, m, of the watchtower.
We can input m into function V to obtain the visibility from watchtower, V(m), in meters. Since visibility indicates the distance you can see, this also gives the distance of the trolls. This can then be input into function T to obtain the time that the Hobbits have to prepare for a troll attack.
Let's find T(V(m)) by substituting the formula for V(m) into function T as shown below.
T(V(M))=T(50m)
=50m/80
We can simplify this as follows:
=50m/80
=5m/8
Actually, the speed of the earth is the same everywhere, taking the angular speed as the valid measure of the speed
If the force and the motion are along the same direction (like it is here) then work is force*distance. The time doesn't come into play until you want the power used. So here
W=9.0*3.0=27J
Answer: 1160 m
Explanation:
Speed = distance / time. Plug in 40 m/s for speed and 29 s for time in order to get the distance, 1160 m.
