One mole of an ideal gas is heated slowly so that it goes from the PV state (Pi, Vi) to (6Pi, 6Vi) in such a way that the pressure is directly proportional to the volume. (a) How much work is done on the gas in the process? (Use any variable or symbol stated above along with the following as necessary: n and R.)W =(b) How is the temperature of the gas related to its volume during this process? (Do not substitute numerical values; use variables only. Use the following as necessary: n, R, V, Vi, and Pi.)T =

One mole of an ideal gas is heated slowly so that it goes from the PV state (Pi, Vi) to (6Pi, 6Vi) in such a way that the pressure is directly proportional to the volume. (a) How much work is done on the gas in the process? (Use any variable or symbol stated above along with the following as necessary: n and R.)W =(b) How is the temperature of the gas related to its volume during this process? (Do not substitute numerical values; use variables only. Use the following as necessary: n, R, V, Vi, and Pi.)T =

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter3: The First Law Of Thermodynamics

Section: Chapter Questions

Problem 97CP: The insulated cylinder shown below is closed at both ends and contains an insulating piston that is...

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The insulated cylinder shown below is closed at both ends and contains an insulating piston that is flee to move on frictionless bearings. The piston divides the chamber into two compartments containing gases A and B. Originally, each compartment has a volume of 5.0102 m3 and contains a monatomic ideal gas at a temperature of and a pressure of 1.0 atm. (a) How many moles of gas are in each compartment? (b) Heat Q is slowly added to A so that it expands and B is compressed until the pressure of both gases is 3.0 atm. Use the fact that the compression of B is adiabatic to determine the final volume of both gases. (c) What are their final temperatures? (d) What is the value of Q?
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In this problem you are to consider an adiabaticexpansion of an ideal diatomic gas, which means that the gas expands with no addition or subtraction of heat. Assume that the gas is initially at pressure p0, volume V0, and temperature T0. In addition, assume that the temperature of the gas is such that you can neglect vibrational degrees of freedom. Thus, the ratio of heat capacities is γ=Cp/CV=7/5. Note that, unless explicitly stated, the variable γshould not appear in your answers--if needed use the fact that γ=7/5 for an ideal diatomic gas. Find an analytic expression for p(V), the pressure as a function of volume, during the adiabatic expansion. Express the pressure in terms of V and any or all of the given initial values p0, T0, and V0. p(V) = __________
In this problem you are to consider an adiabaticexpansion of an ideal diatomic gas, which means that the gas expands with no addition or subtraction of heat. Assume that the gas is initially at pressure p0, volume V0, and temperature T0. In addition, assume that the temperature of the gas is such that you can neglect vibrational degrees of freedom. Thus, the ratio of heat capacities is γ=Cp/CV=7/5. Note that, unless explicitly stated, the variable γshould not appear in your answers--if needed use the fact that γ=7/5 for an ideal diatomic gas. A) Find an analytic expression for p(V), the pressure as a function of volume, during the adiabatic expansion. Express the pressure in terms of V and any or all of the given initial values p0, T0, and V0. p(V) = __________ B) At the end of the adiabatic expansion, the gas fills a new volume V1, where V1>V0. Find W, the work done by the gas on the container during the expansion. Express the work in terms of p0, V0, and V1. Your…
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