At 32°C and 205 kpa gauge. The specific weight of a certain gas was 13.7 N/m³. Determine the gas constant of this gas.
answer = 718.87 J/kg K.
Comment/likes if you want the step by step solution of the given problem.
T= 32 + 273 = 305 K
P absolute = 205 + 101.325 = 306.325 kPa
Specific weight = 13.7 N/m3
Mass density = 13.7/9.81 = 1.397 kg/m3
R= P/(mass density × T)
R= 306,325 Pa / (1.397 kg/m3 × 305 K)
R= 718.93 J/kg.K
answer = 718.87 J/kg K.
Step by step solution please
Bat 481.12 J/kg.K nakukuha ko? Huhu
Ah gets. Wala kasing atmospheric pressure sa module namin na nalagay si sir.
To determine the gas constant of the given gas, we can use the ideal gas law equation, which states:
PV = nRT
Where:
P - Pressure
V - Volume
n - Number of moles of gas
R - Gas constant
T - Temperature
In this case, we are given the temperature (32°C) and pressure (205 kPa gauge) as well as the specific weight of the gas (13.7 N/m³).
First, let's convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 32 + 273.15 = 305.15 K
Next, let's convert the pressure from kPa gauge to kPa absolute:
P(absolute) = P(gauge) + Atmospheric pressure
Note that atmospheric pressure is typically around 101.3 kPa.
P(absolute) = 205 + 101.3 = 306.3 kPa
Now, let's determine the density (ρ) of the gas using the specific weight (γ) formula:
γ = ρ * g
where:
γ - specific weight
ρ - density
g - acceleration due to gravity (approximately 9.8 m/s²)
ρ = γ / g
ρ = 13.7 / 9.8 = 1.3979 kg/m³
Now, let's determine the molar mass (M) of the gas using the ideal gas law rearranged equation:
PV = nRT
nRT = PV
M = (PV) / (RT)
where:
M - Molar mass of the gas
Rearranging the equation:
M = (P * V) / (n * R * T)
Since we are trying to determine the gas constant (R), we can rearrange the equation again:
R = (P * V) / (n * M * T)
Plugging in the given values:
R = (306.3 * V) / (n * 1.3979 * 305.15)
Since the volume (V) is not provided, it is impossible to find the precise value of the gas constant (R). However, we can calculate it relative to the volume of the system. So, if we assume a specific value for the volume, we can determine the corresponding value for the gas constant.