To determine the speed of sound in helium, we will use the formula for the speed of sound in a gas, which is given by:
V=√γPρ
Where:
- V is the speed of sound,
- γ is the adiabatic index (ratio of specific heats),
- P is the pressure,
- ρ is the density of the gas.
Step 1: Identify the given values
From the problem statement, we have:
- Mass of helium, m=4g=0.004kg (since 1 g = 0.001 kg)
- Volume of helium, V=22.4liters=22.4×10−3m3 (since 1 liter = 0.001 m³)
- Pressure, P=105N/m2
- Adiabatic index for helium, γ=1.67
See AlsoHelium Network FAQ | Helium DocumentationDiscover Helium Mobile Hotspot: Network Building, SimplifiedWhich Helium Miner Is Best? | Helium Mining UKHelium - Introducing the People's NetworkStep 2: Calculate the density (ρ)
The density (ρ) of helium can be calculated using the formula:
ρ=mV
Substituting the values:
ρ=0.004kg22.4×10−3m3
Calculating ρ:
ρ=0.0040.0224≈0.1786kg/m3
Step 3: Substitute the values into the speed of sound formula
Now, we can substitute γ, P, and ρ into the speed of sound formula:
V=√1.67×1050.1786
Step 4: Calculate the speed of sound (V)
Calculating the value inside the square root:
V=√1.67×1050.1786≈√934.6
Calculating the square root:
V≈30.6×10≈967m/s
Final Result
The speed of sound in helium is approximately:
V≈967m/s
- V is the speed of sound,
- γ is the adiabatic index (ratio of specific heats),
- P is the pressure,
- ρ is the density of the gas.
From the problem statement, we have:
- Mass of helium, m=4g=0.004kg (since 1 g = 0.001 kg)
- Volume of helium, V=22.4liters=22.4×10−3m3 (since 1 liter = 0.001 m³)
- Pressure, P=105N/m2
- Adiabatic index for helium, γ=1.67
The density (ρ) of helium can be calculated using the formula:
Now, we can substitute γ, P, and ρ into the speed of sound formula:
Calculating the value inside the square root:
The speed of sound in helium is approximately:
