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4. One mole of helium gas is injected into each side of a slidable, airtight lead piston that separates two chambers of a sealed cylinder. The outside of the cylinder is insulated everywhere except where noted below. The cylinder and piston have lengths and cross- sectional area labeled in the diagram. The helium in the left chamber is heated from outside at a rate of 450 W, and the helium in the other chamber expels heat into a cool region. The full system eventually comes to steady-state. When it reaches steady state, the force needed to hold on the end cap is measured to be 18,000 N, and the piston has slid to an equilibrium point that is a distance x from the left end. force holding cap = 18,000N pressure. cross-sectional area of cylinder = 0.02m² x = ? Imol He b. Find the distance x. dQ dt =+450W 45cm 15cm lead piston a. Find the temperature difference of the two chambers. Assume helium behaves as an ideal gas, and that heat transfer through the container walls is instantaneous (but not through the lead piston). The thermal conductivity of lead is 35 W/m-K. The force holding the cap accounts for all forces on it, including atmospheric dQ dt c. Find the temperature of the lead piston at its center. 1mol He =-450W

4. One mole of helium gas is injected into each side of a slidable, airtight lead piston that separates two chambers of a sealed cylinder. The outside of the cylinder is insulated everywhere except where noted below. The cylinder and piston have lengths and cross- sectional area labeled in the diagram. The helium in the left chamber is heated from outside at a rate of 450 W, and the helium in the other chamber expels heat into a cool region. The full system eventually comes to steady-state. When it reaches steady state, the force needed to hold on the end cap is measured to be 18,000 N, and the piston has slid to an equilibrium point that is a distance x from the left end. force holding cap = 18,000N pressure. cross-sectional area of cylinder = 0.02m² x = ? Imol He b. Find the distance x. dQ dt =+450W 45cm 15cm lead piston a. Find the temperature difference of the two chambers. Assume helium behaves as an ideal gas, and that heat transfer through the container walls is instantaneous (but not through the lead piston). The thermal conductivity of lead is 35 W/m-K. The force holding the cap accounts for all forces on it, including atmospheric dQ dt c. Find the temperature of the lead piston at its center. 1mol He =-450W

Elements Of Electromagnetics
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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**Problem 4:** One mole of helium gas is injected into each side of a slidable, airtight lead piston that separates two chambers of a sealed cylinder. The outside of the cylinder is insulated everywhere except where noted below. The cylinder and piston have lengths and cross-sectional areas labeled in the diagram. The helium in the left chamber is heated from outside at a rate of 450 W, while the helium in the other chamber expels heat into a cooler region. The entire system eventually reaches a steady state. At steady state, the force needed to hold on the end cap is measured to be 18,000 N, and the piston settles at an equilibrium point that is a distance \( x \) from the left end. **Diagram Description:** - The cylinder is broken into two sections by a lead piston. - The left chamber contains 1 mole of helium, heated at a rate of 450 W. - The right chamber contains 1 mole of helium, expelling heat at 450 W. - Total length of the cylinder is 45 cm, with the lead piston measuring 15 cm. - The cross-sectional area of the cylinder is \( 0.02 \, \text{m}^2 \). - The force required to hold the end cap is 18,000 N. **Assumptions:** - Helium behaves as an ideal gas. - Heat transfer through the container walls is instantaneous, except through the lead piston. - The thermal conductivity of lead is 35 W/m·K. - The force on the cap incorporates all acting forces, including atmospheric pressure. **Problems:** a. Determine the temperature difference between the two chambers. b. Calculate the distance \( x \) of the piston from the left end. c. Find the temperature of the lead piston at its center.
Transcribed Image Text:**Problem 4:** One mole of helium gas is injected into each side of a slidable, airtight lead piston that separates two chambers of a sealed cylinder. The outside of the cylinder is insulated everywhere except where noted below. The cylinder and piston have lengths and cross-sectional areas labeled in the diagram. The helium in the left chamber is heated from outside at a rate of 450 W, while the helium in the other chamber expels heat into a cooler region. The entire system eventually reaches a steady state. At steady state, the force needed to hold on the end cap is measured to be 18,000 N, and the piston settles at an equilibrium point that is a distance \( x \) from the left end. **Diagram Description:** - The cylinder is broken into two sections by a lead piston. - The left chamber contains 1 mole of helium, heated at a rate of 450 W. - The right chamber contains 1 mole of helium, expelling heat at 450 W. - Total length of the cylinder is 45 cm, with the lead piston measuring 15 cm. - The cross-sectional area of the cylinder is \( 0.02 \, \text{m}^2 \). - The force required to hold the end cap is 18,000 N. **Assumptions:** - Helium behaves as an ideal gas. - Heat transfer through the container walls is instantaneous, except through the lead piston. - The thermal conductivity of lead is 35 W/m·K. - The force on the cap incorporates all acting forces, including atmospheric pressure. **Problems:** a. Determine the temperature difference between the two chambers. b. Calculate the distance \( x \) of the piston from the left end. c. Find the temperature of the lead piston at its center.
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