An ideal gas in a cylinder expands against a constant external pressure of 1.00

Question

An ideal gas in a cylinder expands against a constant external pressure of 1.00 atm from a volume of 3.63 L to a volume of 9.07 L at a constant temperature.

a. Determine the initial pressure of the gas, in atm
Pinitial = 2.50 atm

b. Calculate w (in J) associated with the expansion of the ideal gas.
(please include the proper sign with your answer) ,
w = J

c. The piston is connected to a paddle which turns in a 1.00 L (1000 g) container of water at 25.0oC. Calculate the change in temperature of the water brought about by the turning of the paddle. assuming that all of the work done by the system is changed into heat which is transferred to the water.
(This is very similar to the experiment carried out by Joule to demonstrate the interconversion of heat and work, i.e. the 1st Law of Thermodynamics.)
?T = oC

Explanation / Answer

(a)

Isothermal process

V1=3.63L

P2=Pext=1atm

V2=9.07L

P1=P2*V2/V1=2.5atm

(b)

Pext=1atm=1.01235*10^5N/m2

V2=9.07*10^-3m3

V1=3.63*10^-3m3

Work done = w = -Pext*(V2-V1)=

-101.325*(9.07-3.63)=-551.2j

(c)

Isothermal process, dU=0

q=-w+dU=-w=551.2J

q=m*cp*dT

Mass of water =m=1kg

Specific heat of water, cp=4.18*10^3J/kg-C

change in temperature, dT= q/(m*cp)=551.2/(1*4.18*10^3)=

0.132C

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