An expandable cylinder has its top connected to a spring with force constant 2.00 x 10 N/m (see figure below). The cylinder is filled with 5.50 L of gas with the spring relaxed at a pressure of 1.00 atm and atemperature of 20.0°C.T= 20.0°CT(a) If the lid has a cross-sectional area of 0.0100 m2 and negligible mass, how high will the lid rise when the temperature is raised to T,= 290°C?cm(b) What is the pressure of the gas at T, = 290°C?PaNeed Help?Read Itww

Given data: The value of spring constant is k=2.00x103 N/m. The initial volume of the gas filled in the cylinder is V1=5.50 L. The initial pressure of the gas is P1=1.00 atm. The initial temperature of the lid is T1=20oC. The cross sectional area of the lid is A=0.0100 m2. The final temperature of the lid is Tf=290oC. The expression for the final pressure of the gas can be calculated as, P2=P1+k×hA The expression for the final volume of the gas filled in the cylinder can be calculated as, V2=V1+h×A The expression for the height of the lid raised when the temperature is raised to Tf=290oC can be calculated as, P1V1T1=P2V2TfP1V1T1=P1+k×hA×V1+h×ATfP1V1TfT1=P1V1+P1h×A+k×hAV1+k×h2P1V1TfT1-1=P1×h×A+k×hAV1+k×h2Substitute the known values in the above expression. 1.00 atm×101325 N/m21 atm×5.50 L×10-3 m31 L×290oC+273 K20oC+273 K-1=1.00 atm×101325 N/m21 atm×h×0.0100 m2+2.00×103 N/m×h0.0100 m2×5.50 L×10-3 m31 L+2.00×103 N/m×h2513.54 N·m=10132.5 N×h+1100 N×h+2000 N/m×h2 513.54 N·m=11232.5 N×h+2000 N/m×h2 By solving the above expression with the help of calculator. h=0.045 m×100 cm1 mh=4.5 cm Thus, the height of the lid raised when the temperature is raised to Tf=290oC is 4.5 cm.Part-(b) The expression for the pressure of the gas at Tf=290oC can be calculated as, P2=P1+k×hA Substitute the known values in the above expression. P2=1.00 atm×101325 N/m21 atm+2.00×103 N/m×0.045 m0.0100 m2P2=110325 N/m2×PaN/m2P2=110325 Pa Thus, the pressure of the gas at Tf=290oC is 1103215 Pa.

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An expandable cylinder has its top connected to a spring with force constant 2.00 x 103 N/m (see figure below). The cylinder is filled with 5.50 L of gas with the spring relaxed at a pressure of 1.00 atm and a temperature of 20.0°C. T= 20.0°C (a) If the lid has a cross-sectional area of 0.0100 m2 and negligible mass, how high will the lid rise when the temperature is raised to T,= 290°C? cm (b) What is the pressure of the gas at T, = 290°C? Pa

An expandable cylinder has its top connected to a spring with force constant 2.00 x 103 N/m (see figure below). The cylinder is filled with 5.50 L of gas with the spring relaxed at a pressure of 1.00 atm and a temperature of 20.0°C. T= 20.0°C (a) If the lid has a cross-sectional area of 0.0100 m2 and negligible mass, how high will the lid rise when the temperature is raised to T,= 290°C? cm (b) What is the pressure of the gas at T, = 290°C? Pa

College Physics

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Molecule, is a collection of two or more atoms together (which constitute the smallest observable unit) into a pure material. There are some ways to represent the structure of a molecule. Factor symbols represent atoms in Lewis structures, and dots represent electrons that accompany them. A pair of mutual electrons (covalent bond) may be represented by a single dash. The ball-and-stick model depicts the spatial structure of the atoms better.

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An expandable cylinder has its top connected to a spring with force constant 2.00 x 10 N/m (see figure below). The cylinder is filled with 5.50 L of gas with the spring relaxed at a pressure of 1.00 atm and a
temperature of 20.0°C.
T= 20.0°C
T
(a) If the lid has a cross-sectional area of 0.0100 m2 and negligible mass, how high will the lid rise when the temperature is raised to T,= 290°C?
cm
(b) What is the pressure of the gas at T, = 290°C?
Pa
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