If the specific volume of a certain gas is 0.7848 m3/kg, what is its specific weight?
The correct answer and explanation is :
To calculate the specific weight of a gas, we can use the relationship between specific volume and specific weight.
Formula:
[
\gamma = \frac{g}{v}
]
where:
- (\gamma) is the specific weight (in Newtons per cubic meter, (N/m^3)),
- (g) is the acceleration due to gravity, approximately (9.81 \, m/s^2),
- (v) is the specific volume (in cubic meters per kilogram, (m^3/kg)).
Alternatively, the specific weight can be calculated using the inverse of specific volume multiplied by the acceleration due to gravity:
[
\gamma = \frac{g}{v}
]
Given:
- Specific volume (v) = 0.7848 m³/kg.
Step-by-Step Calculation:
- Formula application:
[
\gamma = \frac{9.81 \, \text{m/s}^2}{0.7848 \, \text{m}^3/\text{kg}}
] - Perform the division:
[
\gamma = 12.5 \, \text{N/m}^3
]
Thus, the specific weight of the gas is 12.5 N/m³.
Explanation:
The specific weight of a substance is the weight per unit volume, essentially telling us how heavy a specific volume of that substance is. To find the specific weight of a gas, we use the formula (\gamma = \frac{g}{v}), where the specific volume ((v)) is given in cubic meters per kilogram and we multiply by the gravitational constant to account for weight.
In this case, we were provided with a specific volume of 0.7848 m³/kg. Using this value, we calculated that the specific weight of the gas is 12.5 N/m³. This means that each cubic meter of the gas weighs 12.5 Newtons.
The concept of specific weight is important in many applications, including fluid mechanics, thermodynamics, and engineering, as it helps in determining how much force or weight a particular volume of gas will exert under the influence of gravity.