Please answer all questions and show all work! 9. A gas is contained in a chambe

Question

Please answer all questions and show all work!

9. A gas is contained in a chamber such as that in the figure. Suppose that the region outside the chamber is evacuated and the total mass of the block and the movable piston is 175 kg. When 2180 J of heat flows into the gas, the internal energy of the gas increases by 1760 J. What is the distance (s) through which the piston rises? ama Movable piston- Vi F=PA F-PA 10. The work done by six moles of a monatomic ideal gas (? = 5/3) in expanding adiabatically is 970 J. The initial temperature and volume of the gas are 375 K and 0.130 nm. What is the final volume of the gas? Hint: For an adiabatic proces-T1V1y-1 T-V m3

Explanation / Answer

Q9.

as per first law of thermodynamics,

energy supplied=change in internal energy+work done

==.work done=2180-1760=420 J

as work done=force*distance

=mass of the block and movable piston*g*distance

==>420=175*9.8*distance

==>distance=0.245 m

Q10

number of moles=n=6

gamma=5/3

work done =W=970 J

initial temperature=T1=375 K

initial volume=V1=0.13 m^3

initial pressure=P1=n*R*T1/V1

=6*8.314*375/0.13

=1.439*10^5 N/m^2

then the constant for adiabatic process =K=P1*V1^(gamma)

=1.439*10^5*0.13^(5/3)

=4800.6

let final volume be V2.

work done=K*(V2^(1-gamma)-V1^(1-gamma))/(1-gamma)

using the values,

970=4800.6*(V2^(-2/3)-V1^(-2/3))/(-2/3)

==>V2=0.13704 m^3

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