Please help me with this problem A cylinder with a piston contains 0.159 mol of

Question

Please help me with this problem

A cylinder with a piston contains 0.159 mol of nitrogen at a pressure of 1.83 Times 10^5 Pa and a temperature of 350 K. The nitrogen may be treated as an ideal gas. The gas is first compressed isobaric ally to half its original volume. It then expands adiabatically back to its original volume, and finally it is heated isochoric ally to its original pressure. Compute the temperature at the beginning of the adiabatic expansion. T_1 = 175 K Compute the temperature at the end of the adiabatic expansion. Compute the minimum pressure.

Explanation / Answer

initial pressure=P0=1.83*10^5 Pa

initial temperature=T0=350 K

number of moles=n=0.159

then initial volume=V0=n*R*T0/V0=2.5283*10^(-3) m^3

step 1:isobaric compression:

pressure remains constant.

so P1=1.83*10^5 Pa

volume becomes half.

V1=V0/2=1.26415*10^(-3) m^3

temperature=T1=P1*V1/(n*R)=175 K

step 2:

adibatic expansion:

volume back to original.

so V2=V0=2.5283*10^(-3) m^3

nitrogen is a diatomic gas.

vaue of specific heat=gamma=1.4

as for adiabatic process, pressure*volume^(gamma)=constant

==>P1*V1^1.4=P2*V2^1.4

==>P2=69344.033 Pa

then temperature =T2=P2*V2/(n*R)=132.626 K

step 3:

isochoric heating

so pressure changes to P0

answers are:

part A:
T1=175 K

part B:

T2=132.626 K

part C:

minium pressure=P2=69344.033 Pa

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