proofs Flashcards
1
Q
prove that
pV = NkT
A
pV = nRT
pV = n (Na k) T
pV = NkT
2
Q
prove that
pV = 1/3 Nm<v^2>
A
- -mv - mv = 2mv
- no. of collisions = v / 2L
- force = 2mv (v/2L) = (mv^2)/L
- pressure = F/A = (mv^2)/(LA) = (mv^2)/ V
- p = mN<v^2> / V
- pV = mN<v^2> (x1/3)
- pV = 1/3 mN<v^2>
3
Q
prove that
1/2 m <v^2> = 3/2 kT
A
- NkT = 1/3 mN<v^2>
- 3kT = m<v^2> (x 1/2)
- 3/2 kT = 1/2 m<v^2>
4
Q
prove that
V (rms) = √(3RT)/Mr
A
- 3kT = m<v^2>
- (3kT)/m = <v^2>
- (3RT)/mNa = <v^2>
- √(3RT)/Mr = <v^2>
5
Q
prove that
p = 1/3 ρ<v^2>
A
- pV= 1/3 Nm<v^2>
- p = (1/3 Nm<v^2>) / V
- p = 1/3 ρ<v^2>
6
Q
prove that
ω = 2π/T = 2πf
A
- ω = θ/t
- ω = S/rt
- ω = 2πr/rt
- ω = 2π/T = 2πf
7
Q
prove that
v = ωr
A
- ω = θ/t
- ω = S/rt
- ω = v/r
- v = ωr
8
Q
prove that
a(c) = vω = v^2/r = ω^2xr
A
- a(c) = δv / δt
- a(c) = vδθ / δt = vθ
- a(c) = v x (v/r) = v^2 /r
- a(c) = ωrω = ω^2 x r
9
Q
prove that
F(c) = mvω = mv^2 / r = mω^2r
A
- F(c) = ma = mvω
- F(c) = ma = mv^2 /r
- F(c) = ma = mω^2r
10
Q
prove that
a = -ω^2 X
A
- X = r cos(ωt)
- v = -rω sin(ωt)
- a = -rω^2 cos(ωt)
- a = -ω^2 X
11
Q
prove that
v^2 = ω^2(A^2 - X^2)
A
- sin(ωt) = (√(r^2-X^2)) / r
- v^2 = ωr = ω√(A^2 - X^2) = 2πf√(A^2 - X^2)
- v^2 = ω^2(A^2 - X^2)
12
Q
prove that
T = 2π√(m/k)
A
- F = kX , F = ma
kX = ma - a upwards = kX / m
- a in X direction = -kX / m
- SHM equation –> a = -ω^2 X
-ω^2X = -kX/m - ω^2 = k/m , T = 2π / ω
- T = 2π√(m/k)
13
Q
prove that
T = 2π√(l/g)
A
- F = mgX/l , F = ma
mgX/l = ma - a to zero = gX/l
- a in x direction = -gX/l
- SHM equation –> a = -ω^2X
-ω^2X = -gX/l - ω^2 = g/l , T = 2π/ω
- T = 2π√(l/g)
