Ten moles of a gas are cooled at a constant pressure of 20 bar. The initial temperature is 400 K and the final temperature is 300 K. The gas is known to follow the equation of state: V = RT/P + aP2, where a=0.01 L/bar2mol.
A) Prove that (dU/dT)P is equal to CP - P(dV/dT)P. You may use this equality in solving other test problems even if you are unable to prove it.
B) Find ?U for the gas in this process.
C) Find ?S for the gas in this process.
The ACTUAL heat capacity for the gas at the pressure P=20 bar is constant and equal to CP=75 J/mol-K.
Apply expansion rule to ((??U)/?T)_P:
Comparing this expansion with the fundamental property relationship for internal energy:
Evaluate ((??V)/?T)_P where ?V=RT/P+aP^2 according to the equation of state:
Substitute into ((??U)/?T)_P expression:
Integrate with respect to T:
To find ((??S)/?T)_P of the gas, write a total derivative:
Where ((??S)/?P)_T=-((??V)/?T)_P according to Maxwell’s relations, and ((??S)/?T)_P=C_P/T , since CP is by definition a partial derivative of molar enthalpy and can be related to a partial derivative of molar entropy
You might also like to view...
The final drive ring and pinion gears in a typical transaxle are of the ________ type?
A) Helical B) Hypoid C) Spiral bevel D) Both B and C
330 lb × 100 ft = ____________________ lb/ft per minute = ____________________ lb/ft per second = ____________________ HP
Fill in the blank(s) with the appropriate word(s).
An electronic power steering (EPS) system is being discussed. Technician A says if the engine stalls and the ignition switch is on, the EPS remains operational. Technician B says if the steering wheel is turned and held fully in one direction, the power module reduces current flow through the steering gear motor to prevent motor overheating. Who is correct?
A. A only B. B only C. Both A and B D. Neither A nor B
What law says employers must provide information about hazardous materials used in the work place?
A) Right to know B) EPA C) OSHA D) RCRA