~christina~

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**1. Homework Statement**

One mole of helium is enclosed in a cylinder with a movable piston. By placing the cylinder in contact with various reservoirs and also insulating it at proper times, the helium performs a cycle. Compute the internal energy change, heat transferred, and work perfomed for each segment of the cyle and the total amount of each of these quantities for the entire cyle. Assume helium to be an ideal gas.

http://img179.imageshack.us/img179/4843/graphnc4.th.jpg [Broken]

**2. Homework Equations**

[tex]\Delta U= Q + W [/tex]

PV= nRT

[tex]Q= nC_p \Delta T[/tex]

[tex] Q= nC_v \Delta T[/tex]

[tex]\gamma= C_p / C_v = 1.67[/tex]

[tex]C_v= 3/2R [/tex]

[tex]C_p= 5/2R[/tex]

**3. The Attempt at a Solution**

B is unknown but not sure how to find it...

I do have Parts:

A=> P= 8.00x10^4Pa, V= 2.00m^3

B=> P= ? V=?

C=> P= 3.00x10^4 Pa, V= 5.00m^3

D=> P= 3.00x10^4 Pa, V= 2.00m^3

__For DA which is isovolumetric__w= 0

[tex]\Delta U= Q [/tex] for U

[tex]\Delta Q= nCv (T_D-T_A) [/tex] for finding heat (Q)

[tex] \Delta E_{int}= C_v \Delta T[/tex] => however I'm not given T so what do I do?

do I use PV= nRT and then solve for T since I have P and V ? so

[tex] \Delta P V /nR = \Delta T[/tex]

__For CD which is Isobaric__P= constant

[tex]W= -P(V_F-V_i) [/tex] for the internal E

[tex] \E_{int}= Q + W [/tex] for the work

[tex] PV= nRT [/tex]

[tex] Q= nCP \Delta T [/tex]

[tex] \E _{int}= ? [/tex] not sure about this

**For the part AB It is isothermic**T= constant

[tex]T_A= T_B [/tex]

[tex]\Delta U= nR\Delta T= 0 [/tex] internal Energy which is = 0

so based on above [tex] Q= -W[/tex] to find the heat

[tex]P_A= 8.00x10^4 Pa [/tex]

[tex]P_A= 2.00 m^3 [/tex]

[tex]W= nRT ( /frac{V_A} {V_B}) [/tex] => don't have V for the final VB

__For part BC__It's adiabatic so Q= 0 thus

[tex] \Delta U= W [/tex]

point B is not known (P or V) initial point

C=> P= 3.00x10^4 Pa, V= 5.00m^3

[tex]P_iV_i^{\gamma} = P_iV_f^{\gamma}[/tex]

not sure how to find the [tex]\Delta U[/tex] and that would also = W but if I don't find those then how can I find the W?

**Point B**I don't have the P or V for point B so I'm not exactly sure how to find the info I need.

I think that for the [tex]\Delta U= 0 [/tex]

[tex]P_iV_i^{\gamma} = P_fV_f^{\gamma}[/tex]

so I think I can find the V and P. But don't you have to be given [tex]\gamma[/tex] ? or is it a constant?

Well after finding the Pf I was thinking of using the fact that the AB is isothermic and plugging into this..

[tex]Q= W= P_AV_A ln (V_B/V_A)[/tex]

Is this it..I think so but I think I'm missing some things here and there on actually solving this with numbers.

Could someone check it for me?

Thank you.

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