Hi! I tried to organize this as concisely as possible, with the variables defined as well. If you have any questions, please let me know!
- Micro-hydro generator
Variables:
η = efficiency (0.10)
ρ = water density (1000 kg/m³)
g = gravity (10 m/s²)
Q = flow rate (10 m³/s)
h = height (8 m)
Process:
Power from falling water → P=ηρgQhP = ηρgQhP=ηρgQh
=0.10×1000×10×10×8=80,000= 0.10 × 1000 × 10 × 10 × 8 = 80{,}000=0.10×1000×10×10×8=80,000 W = 80 kW
- Gas mass in room
Variables:
P = pressure (10⁵ Pa)
v = average molecular speed (750 m/s)
ρ = gas density
V = volume (1.5 L = 1.5×10⁻³ m³)
Process:
From kinetic theory → P=1/3ρv2P = 1/3 ρv²P=1/3ρv2
Solve density: ρ=3P/v2ρ = 3P/v²ρ=3P/v2
Mass: m=ρVm = ρVm=ρV
Result → 0.8 g
- Concave mirror image shift
Variables:
f = focal length (250 mm)
u = object distance
v = image distance
Process:
Mirror formula → 1/f=1/u+1/v1/f = 1/u + 1/v1/f=1/u+1/v
At u = 375 mm → v = 750 mm
At u = 400 mm → v ≈ 667 mm
Shift = 750 − 667 ≈ 83 mm
- Photoelectric effect
Variables:
h = Planck’s constant
ν = frequency (10¹⁶ Hz)
E = photon energy
φ = work function
K = kinetic energy
Process:
Photon energy → E=hν=6.6×10−18E = hν = 6.6×10⁻¹⁸E=hν=6.6×10−18 J
Given φ = 1/3 E
So K=E−φ=2/3EK = E − φ = 2/3 EK=E−φ=2/3E
Result → 4.4 × 10⁻¹⁸ J
