A 0.8-m³ rigid tank contains carbon dioxide (CO₂) gas at 250 K and 100 kPa. A 500-W electric resistance heater placed in the tank is now turned on and kept on for 40 min after which the pressure of CO₂ is measured to be 175 kPa. Assuming the surroundings to be at 300 K and using constant specific heats, determine (a) the final temperature of CO₂, (b) the net amount of heat transfer from the tank, and (c) the entropy generation during this process.

Explanation:

Given:

Power, p = 500 W

Time, t = 40 min

= 2400 s

Volume, V = 0.8 m^3

Temperature, T = 250 K

Pressure, P = 100 kPa

Temperature of surroundings, Ts = 300 K

Using ideal gas equation,

PV = nRT

n = (100 × 10^3 × 0.8)/(8.3145 × 250)

= 38.49 mole

Mass = number of moles × molar mass

Molar mass = 12 + (16 × 2)

= 44 g/mol

Mass = 44 × 38.49

= 1693.43 g

= 1.693 kg.

A.

P2 = 175 kPa

Using pressure law,

P1/T1 = P2/T2

T2 = (175 × 250)/100

= 437.5 K

B.

Cvco2 = 0.706 kJ/kg.K

Total energy, U = Qin - Qout

Qout = (p × t) - (m × cv × delta T)

= (500 × 2400) - (1.693 × 0.706 × (437.5 - 250))

= 1200 kJ - 224.11 kJ

= 975.889 kJ

= 975.9 kJ

C.

Cpco2 = 0.895 kJ/kg.K

Gas constant, Rc = R/molar mass of CO2

= 8.3145/44

= 0.189

Using the formula ,

Entropy, S = (m × (Cpco2 × ln(T2/T1) - Rc × ln(P2/P1)) + Qout/Ts

Inputting values,

= (1.693 × (0.895 × ln(437.5/250) - 0.189 × ln(175/100)) + 975.9/300

= 3.922 kJ/K.

3. dark matter

empty space could also be a simple vacuum