High School

During a polytropic process with \( n = 1.3 \), nitrogen gas goes from 400 K and 200 kPa to 800 K. What is the approximate specific work done by the gas during this process?

a) 66.9 kJ/kg
b) 72.1 kJ/kg
c) 69.4 kJ/kg
d) 71.8 kJ/kg

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.

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