How Far Will the Spring Compress When the Gas Temperature Rises to 100°C?

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Homework Help Overview

The problem involves a horizontal piston connected to a spring, where the spring's compression is to be determined as the temperature of the gas increases from 20°C to 100°C. The scenario includes parameters such as the spring constant, cross-sectional area of the cylinder, and the amount of gas present.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the relationship between pressure, volume, and temperature using the ideal gas law. There are attempts to relate the force exerted by the gas on the spring to the spring's compression through Hooke's Law. Some participants question the definitions of pressure and the necessary unit conversions.

Discussion Status

The discussion is ongoing, with participants providing hints and asking clarifying questions. There is no explicit consensus, but some guidance regarding unit conversions and the relationship between pressure and force has been offered.

Contextual Notes

Participants note the importance of unit consistency, particularly in converting pressure and volume units, as well as the need to show work for the solution process. There is mention of a previous similar problem that involved a quadratic equation.

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Homework Statement


A horizontal piston is attached to a spring with a spring constant of 1500N/m. The cross sectional area of the cylinder is A=10cm^2, it contains 0.0040mol of gas. At 20 deg Celsius the spring is neither compresssed nor stretched. How far is the spring compressed, x, if the gas temperature is raised to 100 deg celsius?


Homework Equations


PV=nRT ...(P_1 * V_1)/T_1 = (P_2 * V_2)/T_2


The Attempt at a Solution


I assume that the increased volume V_2 = V_1 + Ax. And P_1 is standard pressure, and i need to work in Kelvins, but I have tried everything I know to get the right answer but can not.
I know the answer via the back of our textbook which is 1.02cm. But it is a problem we need to show our work on, and I can't figure this one out. Any help would be greatly appreciated.
 
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What's the definition of pressure? What would the force applied on the spring be equal to (Hint: Consider Hooke's Law) ?
 
Also be very careful re units--this came up recently in a similar problem, where atmospheres of pressure need to converted to Bars, and volume units made to be the same, eg 1 liter is a 1000cm^3.
JS
 
yeah, Pressure = F/A, and F = -kx => -kx/A must equal the pressure exerted by the spring. I have all my units in Pa, m^3, and K, i really don't know where I am going wrong,
 
last time this came up, the soln was a quadratic, maybe if you posted the completed eqn with all the subs and algebra, we may me able to comment
 

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