Question
Asked Oct 21, 2019

#6.19 from book "thermodynamics and statistical mechanics"

 

6.19. An ideal gas in contact with a heat/temperature bath is suddenly and instantan-
eously compressed to ten times its original pressure. What is the minimum heat
that the bath removes per mole of liquid?
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6.19. An ideal gas in contact with a heat/temperature bath is suddenly and instantan- eously compressed to ten times its original pressure. What is the minimum heat that the bath removes per mole of liquid?

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Step 1

An ideal gas is the gas which obeys’s ideal gas law. As it is in contact with heat/temperature bath it means temperature of the gas will remain constant. Ideal gas law is shown below:

Where P represents pressure

             V represents volume

             n represents number of moles

            R represents gas constant

            T represents temperature

PV nRT(1
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PV nRT(1

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Step 2

From the first law of thermodynamic

Where E represents  internal energy

             Q represents heat

             W represents work done

Internal energy is point function (which dependent only on initial and final state of the system) or property. While Q and W both are the path functions ( which dependents on path not on initial and final state).

AE 8Q+6W -(2)
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AE 8Q+6W -(2)

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Step 3

 

As ideal gas in contact with heat/temperature bath means temperature is constant.

There...

AE=6Q+6W
0-8Q+6W
8Q-6W (3)
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AE=6Q+6W 0-8Q+6W 8Q-6W (3)

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