Answer :
Final answer:
The approximate specific work done by the nitrogen gas during the polytrophic process is -72.12 kJ/kg.
Explanation:
To find the specific work done by the nitrogen gas during the polytrophic process, we can use the formula:
W = (nRT2 - nRT1) / (1-n)
Where:
W is the work done
n is the polytropic index (in this case n = 1.3)
R is the specific gas constant for nitrogen
T1 and T2 are the initial and final temperatures of the gas
Using the given values:
T1 = 400 K, T2 = 800 K
n = 1.3
We can substitute these values into the formula to find the specific work done by the gas:
W = (3 * R * (800 - 400)) / (1 - 1.3) = -72.12 kJ/kg
Therefore, the approximate specific work done by the gas during this process is approximately -72.12 kJ/kg.