Bioengineering Fundamentals-Saterbak Problem 4.3 of Textbook A weight is added t

Question

Bioengineering Fundamentals-Saterbak Problem 4.3 of Textbook

A weight is added to a piston so that the volume of the gas inside the container is reduced from 2.5 L to 1.0 L at a constant temperature. How much heat do you need to add to the system if you want to increase the volume back to 2.5 L at this new pressure? Assume an ideal gas and an inital pressure of 1.0 atm.

PLEASE SHOW WORK AND EXPLAIN. Thanks!

P.s. I've already seen this as an answer and I don't understand it so please don't just repost this:

v1 = 2.5 L

v2 = 1L at constant T

p1v1 = p2v2

p1/p2 = 1/2.5 p1 = 1

so p2 = 2.5 atm

gas is ideal so

PV = nRT

1*2.5 = n*.0821*T

T1 = 30.45/n

Heat = mc*delta T

Explanation / Answer

Sol:-

Given Initial volume ( V1) = 2.5 L

Final volume (V2) = 1.0 L

Pext. = 1.0 atm

Since volume reduces therefore compression of gas takes place .

Now

From Mathematical expression of First law of thermodynamics , we have

delta U = q - w (for compression of gas ) .............(1)

here

delta U = change in internal energy

q = amount of heat and

W = work done on the system

we know at constant Temerature i.e T change in internal energy (i.e delta U )= 0

therefore from equation (1) , we have

q = W ............(2)

For compression of gas

W = Pext. delta V ..............(3)

here delta V i.e change in volume = V2 (final volume) - V1 ( initial volume)

therefore

W = 1.0 atm x ( 1.0 L - 2.5 L )

W = 1.0 atm x ( - 1.5 L )

W = - 1.5 L atm

because 1 L atm = 101 .33 J

therefore

W = - 1.5 x 101.33 J

W = - 151.995 J

W = q = - 151.995 J ( heat evolved ) from equation (2)

Heat evolved i.e q = - 151.995 J

Therefore amount of heat needed to add to the system if you want to increase the volume back? to 2.5 L = + 151.995 J

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