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in Physics by (70.7k points)

One mole of an ideal gas is initially at pressure P1, volume V1, and temperature T1, represented by point A on the PV diagram. The gas is taken around cycle ABCA shown. Process AB is isobaric, process BC is isochoric, and process CA is isothermal.

a. Calculate the temperature T2 at the end of process AB in terms of temperature T1.

b. Calculate the pressure P2 at the end of process BC in terms of pressure P1 and V1.

d. Indicate below all of the processes that result in heat being added to the gas.

____ AB ____ BC ____CA

1 Answer

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a. Since PA = PB and VA/TA = VB/TB giving TB = T2 = T1/2 

b. CA is an isotherm so TA = TC so PAVA = PCVC; P1V1 = P2(V1/2) giving P2 = 2P1 

c. Work is the area under the line. No work is done from B to C so we just need the area under line AB. 

Specifically, W = –P∆V = –P1(V1/2 – V1) = +½P1

d. Heat was added in processes BC and CA, but not in AB. 

BC: W = 0 so ∆U = Q and temperature rises so ∆U is positive 

CA: ∆U = 0 (isotherm) so Q = –W and it is an expansion so W is negative and therefore Q is positive 

AB: Compression so W is + and temperature drops so ∆U is negative and Q = ∆U – W which must be negative 

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