Project ForgeThermodynamics
First Law of Thermodynamics
GATE 2023
Medium
A mixture of two ideal gases X and Y, with molar masses MX=10 kg/kmol and MY=20 kg/kmol, is in a container. Total pressure is 100 kPa, total volume 10 m³, temperature 300 K. If the mass of gas-X is 2 kg, the mass of gas-Y in the container is ______ kg. (Rounded to one decimal place, R̄=8314 J/kmol·K)
4 kg(± 0.3 accepted)
Explanation
Moles of X: nX=2/10=0.2 kmol. Total moles: n=PV/(R̄T)=(100000×10)/(8314×300)≈0.4009 kmol. Moles of Y: nY=0.4009−0.2=0.2009 kmol. Mass of Y=nY×MY=0.2009×20≈4.02 kg.
Source: GATE ME 2023 Official Paper (2023)
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