Calculate the ideal (maximum) efficiency for a heat engine operating between the two temperatures using Equation 1.1.
Calculate QH, the heat added to the gas by the hot reservoir during the isobaric expansion from B to C and the isothermal expansion from C to D. You will need to calculate the following:
We do not know the initial volume, VA, but we can calculate it by measuring the volume of the can and adding the initial volume of air in the cylinder. We will ignore the volume in the tubes.
V=(?r^2 h)_can+(Ah_o )_cylinder
where A is the cross-sectional area of the piston.
Calculate VD using an isobar and the Ideal Gas Law: V_A/T_A =V_D/T_D .
Calculate VC using an Isotherm and the Ideal Gas Law:
PCVC =PDVD
Calculate QC ?D . For an isotherm, Q = nRT ln(Vf /Vi ), and since PV = nRT,
QC ?D = PD VD ln (VD /VC)
Remember that Absolute P = (Gauge P) + (Atmospheric P)
Calculate QB ?C . For an isobar, Q = nCp?T , and since air is a diatomic gas Cp = 5/2 R, and nR = PV/T,
Q_(B?C)=(7/2) (P_D V_D)/T_D (T_C-T_B )
Calculate QH = QB ?C + QC ?D.
Your final answer must be in joules (J)
Calculate the work done by the gas by measuring the Area inside the curve.
Calculate the efficiency e = work done by gas/ heat extracted from hot reservoir.
e=W/Q_H ×100%
How does this compare with the ideal efficiency from Step 4?
Calculate the actual work done on the 200 g mass using W = mgh. Be careful to use only the change in height of the mass. How does this compare to the work done by the gas from part 6? Does the gas do any work other than lifting the 200 g mass?