Question

b) Ethane gas at 1 bar and 25 oC is compressed adiabatically to 55 bar in a steady-state flow process for which W = 10 J mol-1. Assume ethane is ideal gas at its initial state and the residual enthalpy of the gas at its final state is - 3270 J/mol, and its heat capacity is constant (CP = 4.5 R), the temperature of ethane at the final state, i.e., after compression, is

i. 403.3 oC; ii. 403.3 K; iii. 130.1 oC; iv. 130.1 K v. Other

c) Air enters the opening of a jet engine of an airplane flying at Mach 2.2. We want to convert the kinetic energy of the incoming airflow to pressure before the air is introduced to the entrance of a compressor, which is to compress the air stream to a pressure that is slightly higher than that in the combustion chamber. To increase the efficiency of such a conversion of energy, we should design the engine entrance channel as a diffuser so that

i) dP/dx > 0 ii) du/dx < 0; iii) dA/dx < 0; iv) I, ii, and iii ; v) None

Answer BOTH and EXPLAIN WHY

Answer 1

Ethane at initial condition

Pressure = 1 bar

Temperature = 25⁰C

Ethane at final condition

Pressure = 55 bar

Given values

C_p = 4.5R

Also we know that workdone for adiabatic process

Hence option (V) is correct

c)

Kinetic energy can be converted into pressure energy by passing a gas stream through increasing cross sectional area. So, as the fluid passes from low cross-sectional area (A) to high cross sectional area(B), the velocity of the same fluid is different. That is, the fluid is flowing faster at A and slower at B (as the area is less) which causes an accumulation of fluid thereby increasing pressure at B.

Hence

and