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Air expands in a piston-cylinder from 500 kPa to 100 kPa in a polytropic process with n 1.5. The initial temperature and volume of the air are 400 K and 1 m³, respectively. Treat the air as an ideal gas with constant properties at 400 K. How much work is produced by the air during this expansion?

Air expands in a piston-cylinder from 500 kPa to 100 kPa in a polytropic process with n 1.5. The initial temperature and volume of the air are 400 K and 1 m³, respectively. Treat the air as an ideal gas with constant properties at 400 K. How much work is produced by the air during this expansion?

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**Problem Statement:** Air expands in a piston-cylinder from 500 kPa to 100 kPa in a polytropic process with \( n = 1.5 \). The initial temperature and volume of the air are 400 K and 1 m\(^3\), respectively. Treat the air as an ideal gas with constant properties at 400 K. **Question:** How much work is produced by the air during this expansion? **Explanation:** This problem involves calculating the work done during a polytropic process, which is a type of thermodynamic process that follows the relation \( PV^n = \text{constant} \), where \( P \) is pressure, \( V \) is volume, and \( n \) is the polytropic index. The work done in a polytropic process can be calculated using the formula: \[ W = \frac{P_2 V_2 - P_1 V_1}{n - 1} \] Where: - \( P_1 \) and \( P_2 \) are the initial and final pressures, - \( V_1 \) and \( V_2 \) are the initial and final volumes, - \( n \) is the polytropic index. Given the ideal gas nature, additional relations can be derived using the ideal gas law to find final volume or other unknowns if required.
Transcribed Image Text:**Problem Statement:** Air expands in a piston-cylinder from 500 kPa to 100 kPa in a polytropic process with \( n = 1.5 \). The initial temperature and volume of the air are 400 K and 1 m\(^3\), respectively. Treat the air as an ideal gas with constant properties at 400 K. **Question:** How much work is produced by the air during this expansion? **Explanation:** This problem involves calculating the work done during a polytropic process, which is a type of thermodynamic process that follows the relation \( PV^n = \text{constant} \), where \( P \) is pressure, \( V \) is volume, and \( n \) is the polytropic index. The work done in a polytropic process can be calculated using the formula: \[ W = \frac{P_2 V_2 - P_1 V_1}{n - 1} \] Where: - \( P_1 \) and \( P_2 \) are the initial and final pressures, - \( V_1 \) and \( V_2 \) are the initial and final volumes, - \( n \) is the polytropic index. Given the ideal gas nature, additional relations can be derived using the ideal gas law to find final volume or other unknowns if required.
Expert Solution
Step 1

Given:

P1=500kPa

T1=400k

V1= 1m3

P2=100kPa

To find:

Amount of work is produced by the air during expansion.

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