Entropy balance for air stream

[gfd43tg]

Homework Statement

Ten kmol per hour of air is throttled from upstream conditions of 25°C
and 10 bar to a downstream pressure of 1.2 bar. Assume air to be an ideal gas with Cp= (7/2)R.

(a)What is the downstream temperature?
(b)What is the entropy change of the air in J mol-1K-1?
(c)What is the rate of entropy generation in W K-1?
(d)If the surroundings are at 20°C, what is the lost work?

Homework Equations

The Attempt at a Solution

For my entropy balance, I am not sure how to get dS_surr/dt

 

[Chestermiller]

Homework Statement

Ten kmol per hour of air is throttled from upstream conditions of 25°C
and 10 bar to a downstream pressure of 1.2 bar. Assume air to be an ideal gas with Cp= (7/2)R.

(a)What is the downstream temperature?
(b)What is the entropy change of the air in J mol-1K-1?
(c)What is the rate of entropy generation in W K-1?
(d)If the surroundings are at 20°C, what is the lost work?

Homework Equations

The Attempt at a Solution

For my entropy balance, I am not sure how to get dS_surr/dt

If air is an ideal gas, and it's passing through an adiabatic throttle valve, the change in enthalpy per mole is zero, and thus the change in temperature is zero. You used the correct formula to get the change in entropy per unit mass, but you need to correct the temperature term (which is now zero). The rate of entropy generation is just the entropy change per mole times the flow rate.

Chet

 

[gfd43tg]

How do you know its adiabatic? Also, if the temperature doesn't change, this is both an adiabatic and isothermal process??

 

[Chestermiller]

How do you know its adiabatic? Also, if the temperature doesn't change, this is both an adiabatic and isothermal process??

Throttles are usually approximated as adiabatic. Regarding adiabatic and isothermal, yes this change for the air is both. What happens mechanistically is that the expansion cooling to the lower pressure is precisely balanced by the viscous heating in the throttle valve. The net effect is no temperature change. Look up throttling in your thermo book under the version of the first law applicable to open systems operating at steady state.

Chet

 

[gfd43tg]

why is dS/dt for the surroundings zero?

 

[Chestermiller]

why is dS/dt for the surroundings zero?

Because the question really implies "what is the rate of entropy generation within the throttle."

Chet