# HW2 - Homework 2: Due at the beginning of class 02/19/10...

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Homework 2: Due at the beginning of class 02/19/10 Problems 1. You have one mole of monatomic ideal gas in a vertical cylinder with a piston of mass m 1 . The piston has a unit area (area = 1), so the pressure on the gas by the piston is m 1 g (i.e. P 1 = m 1 g ) and balanced by the internal pressure of the gas (ignore the effect of atmospheric pressure). The piston and walls of the cylinder are thermal insulators, so the gas inside the cylinder is thermally isolated from the surrounding ( adiabatic ). Initially the gas is in a state at (P 1 , T 1 , V 1 ). (a) You pour very fine grains of sand, one at a time and compress the gas. One grain of the sand has a mass of dm (assume infinitesimally small) and the total mass of the sand is m 1 . Calculate T 2 and express it with T 1 . m 1 gas T 1 , P 1 , V 1 m 1 gas T 2 , P 2 , V 2 m 1 ( Hint ) You can think of this process by imagining that the mass of the piston is increased from m 1 to 2 m 1 very slowly ( dm at a time). Consider a step from m to m + dm during this process, where m is the mass of the piston at that point. In this step, the state of the gas changes from (P,T,V)

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## This note was uploaded on 05/04/2010 for the course CH 43445 taught by Professor Lim during the Spring '10 term at University of Texas at Austin.

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HW2 - Homework 2: Due at the beginning of class 02/19/10...

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