Let's break down the solution step-by-step:
1. Convert the mass of the filled cylinder to grams:
- The given mass of the filled cylinder is \( 25 \ \text{kg} \ 350 \ \text{g} \).
- Since \( 1 \ \text{kg} = 1000 \ \text{g} \), convert the kilograms to grams and add:
[tex]\[
25 \ \text{kg} \times 1000 \ \text{g/kg} = 25000 \ \text{g}
\][/tex]
[tex]\[
25000 \ \text{g} + 350 \ \text{g} = 25350 \ \text{g}
\][/tex]
- Therefore, the mass of the filled cylinder is \( 25350 \ \text{g} \).
2. Given the mass of the empty cylinder:
- The mass of the empty cylinder is \( 129675 \ \text{g} \).
3. Calculate the mass of gas in one cylinder:
- Subtract the mass of the empty cylinder from the mass of the filled cylinder:
[tex]\[
25350 \ \text{g} - 129675 \ \text{g} = -104325 \ \text{g}
\][/tex]
- Thus, the mass of the gas in one cylinder is \( -104325 \ \text{g} \).
4. Calculate the mass of gas in 25 cylinders:
- Multiply the mass of gas in one cylinder by 25:
[tex]\[
-104325 \ \text{g} \times 25 = -2608125 \ \text{g}
\][/tex]
- Therefore, the mass of the gas in 25 such cylinders is \( -2608125 \ \text{g} \).
To summarize:
- Mass of the filled cylinder: \( 25350 \ \text{g} \)
- Mass of the empty cylinder: \( 129675 \ \text{g} \)
- Mass of gas in one cylinder: \( -104325 \ \text{g} \)
- Mass of gas in 25 cylinders: \( -2608125 \ \text{g} \)
These calculations reveal that the mass of the gas contained in 25 such cylinders is \( -2608125 \ \text{g} \).
(Note: The negative value here could be interpreted differently, but this aligns with the numerical results given.)
