One mole of an ideal gas is compressed isothermally but irreversibly at 130oc from 2.5 bar to 6.5bar in a piston/cylinder device. the work required is 30% greater than the work of reversible, isothermal compression. the heat transferred from the gas during compression flows to a heat reservoir at 25oc. claculate the entropy changes of the gas, the heat reservoir, and δstotal.

Entropy change of gas = -7.944 J/mol*K

Entropy change of the reservoir = 13.96 J/mol*K

Total entropy change = 6.02 J/mol*K

Explanation:

Step 1: Data given

1 mol of ideal gas is compressed isothermally ( = constant temperature)

Temperature : 130 °C

Pressure = 2.6 bar to 6.5 bar

The work required is 30% greater than the work of reversible

The heat transferred from the gas during compression flows to a heat reservoir at 25°C

Step 2: Calculate entropy change for gas

ΔSgas = Cp*ln(T2/T1) - R*ln (P2/P1)

 ⇒ Since the temperature is constant, T2 = T1 so ln(T2/T1) = 0

ΔSgas = - R*ln (P2/P1)

⇒ with R = gas constant =  8.314

⇒ with P1 = initial pressure = 2.5 barr

⇒ with P2 = final pressure = 6.5 bar

ΔSgas = -8.314 *ln(6.5/2.5)

ΔSgas = -7.944 J/mol*K

Step 3: Calculate reversible work done

Reversible work done = R*T*ln (P2/P1)

Reversible work done = 8.314 * 403.15 * ln (6.5/2.5)

Reversible work done = = 3202. 67 J/mol

Step 4: Actual work done

Actual work done = 1.3 * 3202.67 = 4163.47 J/mol

For isothermal compression:

Q = -W

Q = -4163.47 J/mol

Step 5: Calculate entropy change for reservoir

Entropy change for reservoir ΔSres = -Q/Tres = 4163.47 /298.15

ΔSres = 13.96 J/mol*K

Step 6: Calculate total entropy change

ΔStotal = ΔSgas + ΔSres = -7.944 J/mol*K +13.96 J/mol*K

ΔStotal =  6.02 J/mol*K

a rain shadow is a dry region of land on the side that is protected against the prevailing winds of a mountain range. the prevailing winds are the winds that occur most of the time in a particular place of the earth

prevailing winds carry air toward the mountain range. as the air rises up over a mountain range, the air cools, water vapor condenses, and clouds form. on this side of the mountains, called the windward side, precipitation falls in the form of  rain  or snow. this dry air produces a  rain shadow.