Question

A piston-cylinder device initially contains 0.08 m3 of nitrogen gas at 150 kPa and 200°C. The nitrogen is now expanded to a pressure of 80 kPa polytropically with a polytropic exponent whose value is equal to the specific heat ratio (called isentropic expansion). Determine the final temperature and the boundary work done during this process.

Answer 1

`V_2 = 0.125 m^3`

Work done = = 5 kJ

Step-by-step explanation:

Given data:

volume of nitrogen
`v_1 = 0.08 m^3`

`P_1 = 150 kPa`

`T_1 = 200 degree celcius = 473 Kelvin`

`P_2 = 80 kPa`

Polytropic exponent n = 1.4

`(T_2)/(T_1) = [(P_2)/(P_1)]^{(n-1)/(n)`

putting all value

`(T_2)/(473) = [(80)/(150)]^{(1.4-1)/(1.4)`

`\frac{T_2} = 395.23 K = 122.08 DEGREE \ CELCIUS`

polytropic process is given as

`P_1 V_1^n = P_2 V_2^n`

`150* 0.08^(1.4) = 80 * V_2^(1.4)`

`V_2 = 0.125 m^3`

work done
`= (P_1 V_1 -P_2 V_2)/(n-1)`

`= (150 * 0.8 - 80 * 0.125)/(1.4-1)`

= 5 kJ