### Problem Statement1.67. A gas contained within a piston-cylinder assembly, initially at a volume of 0.4 m³, undergoes a constant-pressure expansion at 5 bar, while being slowly heated through the base of the cylinder. During this process, the total amount of heat transfer to the gas is 150 kJ and the increase in potential energy of the piston is 75 kJ. The piston is fabricated from heat-resistant material and it moves smoothly in the cylinder so that there is no friction. Assume that the local atmospheric pressure is 1 bar.**Questions:**a. **Find the final volume of the gas, in m³.**b. **Calculate the boundary work done by the gas, in kJ.**c. **If the initial internal energy (U1) of the gas is 15 kJ, what will be its final internal energy (U2), in kJ?**### Explanation:The problem involves applying principles of thermodynamics to a piston-cylinder system. This system experiences a constant-pressure expansion due to heating. - **Initial Volume (V1):** 0.4 m³- **Pressure:** 5 bar- **Heat Transfer (Q):** 150 kJ- **Increase in Potential Energy (ΔPE):** 75 kJ- **Initial Internal Energy (U1):** 15 kJ**Objective:** Solve for the final volume, boundary work, and final internal energy.### Solving the Problem:**a. Final Volume:**Use the ideal gas law or given conditions for calculations knowing there's a constant-pressure process.**b. Boundary Work:**Boundary work (W) in a piston system at constant pressure can be calculated as:\[ W = P \times (V_2 - V_1) \]Rearrange the equation as necessary based on known values.**c. Final Internal Energy:**Use the first law of thermodynamics:\[ \Delta U = Q - W + \Delta PE \]Substitute known quantities to solve for the change in internal energy, then find \( U2 = U1 + \Delta U \).

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1.67. Given that a gas contained within a piston-cylinder assembly, initially at a volume of 0.4 m3, undergoes a constant-pressure expansion at 5 bar, while being slowly heated through the base of the cylinder. During this process, the total amount of heat transfer to the gas is 150 kJ and increase in potential energy of the piston is 75 kJ. The piston is fabricated from heat-resistant material and it moves smoothly in the cylinder so that there is no friction. Assume that the local atmospheric pressure is 1 bar. a. Find the final volume of the gas, in m3. b. Calculate the boundary work done by the gas, in kJ. c. If initial internal energy (U1) of the gas is 15 kJ, what will be its final internal energy (U2), in kJ?

1.67. Given that a gas contained within a piston-cylinder assembly, initially at a volume of 0.4 m3, undergoes a constant-pressure expansion at 5 bar, while being slowly heated through the base of the cylinder. During this process, the total amount of heat transfer to the gas is 150 kJ and increase in potential energy of the piston is 75 kJ. The piston is fabricated from heat-resistant material and it moves smoothly in the cylinder so that there is no friction. Assume that the local atmospheric pressure is 1 bar. a. Find the final volume of the gas, in m3. b. Calculate the boundary work done by the gas, in kJ. c. If initial internal energy (U1) of the gas is 15 kJ, what will be its final internal energy (U2), in kJ?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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