<jupyter_start><jupyter_text>a. From a to b When the mass is added the syringe goes down a little (Adiabate)b. From b to c when the vial is in hot water the syringe does work and moves the mass upwards (isothermal)c. Syringe moves up a little (adiabatic)d. Syringe falls back down (isothermal)e. V$_{a}$ = V$_{a'}$<jupyter_code>Tube_width = 0.6 #cm
Tube_tp_length = 45 #cm
Vial_width = 2.9 #cm
Vial_height = 5 #cm
Tube_ts_length = 28.5 #cm 
Vial_vol = np.pi*((Vial_width/2)**2)*Vial_height
ts_vol = np.pi*((Tube_width/2)**2)*Tube_ts_length
tp_vol = np.pi*((Tube_width/2)**2)*Tube_tp_length
Vial_vol+ts_vol+tp_vol
Vial_vol
(5.4-2.6)/(np.pi*(1.466/2)**2)
Pa = ufloat(100.52*1e3, 0.01*1e3) #kPa
Pb = ufloat(101.38*1e3, 0.01*1e3) #kPa
Pc = ufloat(103.27*1e3, 0.01*1e3) #kPa
Pd = ufloat(101.35*1e3, 0.01*1e3) #kPa
Paa = ufloat(99.96*1e3, 0.01*1e3)
Ta = ufloat(5.2, 0.1) +273.15 #K
Tb = ufloat(5.1, 0.1)+273.15 #K
Tc = ufloat(43.3, 0.1)+273.15 #K
Td = ufloat(43.4, 0.1)+273.15 #K
Taa = ufloat(5, 0.1)+273.15 #K
Va = ufloat(1.8/1e6, 0.1/1e6) #cm^3
Vb = ufloat(1.4/1e6, 0.1/1e6) #cm^3
Vc = ufloat(4.3/1e6, 0.1/1e6) #cm^3
Vd = ufloat(5.0/1e6, 0.1/1e6) #cm^3
Vaa = ufloat(2.0/1e6, 0.1/1e6) #cm^3
def Work(ps, pe, vs, ve):
    return -((ps+pe)/2)*(ve-vs)
WorkAB = Work(Pa, Pb, Va, Vb)
WorkBC = Work(Pb, Pc, Vb, Vc)
WorkCD = Work(Pc, Pd, Vc, Vd)
WorkDA = Work(Pd, Paa, Vd, Vaa)
WorkAB
WorkBC
WorkCD
WorkDA
sW = sum([WorkAB, WorkBC, WorkCD, WorkDA])
sW/0.003
dU = (3/2)*(Pc*Vc-Pb*Vb)
Qh = dU-0.003
print(Qh)
dU = (3/2)*(Paa*Vaa-Pd*Vd)
Qc = dU-0.003
print(Qc)
(abs(Qh)-abs(Qc))/abs(Qh)<jupyter_output><empty_output>
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