- #1
BobaJ
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Homework Statement
The initial state of 0.1 mol of an ideal monatomic gas is P0=32 Pa and v0=8m3. The final state is P1=1 Pa and V1=64m3. Suppose that the gas undergoes a process along a straight line joining these two states with an equation P=aV+b, where a =31/56 and b=255/7. Plot this straight line to scale on a PV diagram.
Calculate:
a) Temperature T as a function of V along the straight line.
b) The value of V which T is a maximum.
c) The values of T0, Tmax and T1.
d) The heat Q transferred from te Volume V0 to any other volume V along the straight line.
e) The values of P and V at which Q is a maximum.
f) The heat transferred along the line from V0 to V when Q is a maximum.
g) The heat transferred from V at maximum Q to V1.
Homework Equations
It's a monatomic gas, so γ=5/3.
The Attempt at a Solution
I have already solved a), b) and c).
a) $$T=\frac{1}{nR}*(aV^2+b)$$
b) Take the first derivate of the last result and equal it to 0 $$V=32.9 m^3$$
c) Just insert the desires values of V in the equation for T:
$$T_{0}=307.9 K$$
$$T_{max} = 720.8 K$$
$$T_{1} = 76.97 K$$
So, now I'm stuck on point d). For a moment I thought I could just take $$Q = \int^V_{V_{0}} P dV $$ and insert the given equation for P. But I'm not sure.
Thanks for your help.