Related to first law of thermodynamics

Question

An insulated tank initially contains 0.25 kg of a gas with an internal energy of 200 KJ/kg. Additional gas with an internal energy of 300 KJ/kg and an enthalpy of 400 KJ/kg enters the tank until the total mass of the gas contained is 1 kg. The final internal energy (in KJ/kg) of the gas in the tank is ?

a) 250

b) 275

c) 350

d) None of these

Answer 1

There is no data offered for the particular gas (or gases), the pressure, or the temperature.

Knowing that Enthalpy is given by Internal Energy Plus Pressure Times Volume,

one could reason that 400 Kilojoules Per Kilogram might be equated to 300 kJ/kg + PV

for the second gas, which isolates PV as 100 kJ/kg.

If I were taking a final examination and had less than a minute to turn in answers,

I would reason that final Internal Energy might be given as

(0.25 kg)(200 kJ/kg) + (0.75 kg)(300 + 100) kJ/kg (for the one kilogram of mixture mass),

which simplifies to 350 kiloJoules Per 1 kilogram or 350 kJ/kg.