A heat engine extracts heat (𝑄_H) from a thermal reservoir at a temperature of 1000 K and rejects heat (𝑄_L) to a thermal reservoir at a temperature of 100 K, while producing work (𝑊). Which one of the combinations of [𝑄_H, 𝑄_L and 𝑊] given is allowed? 

Which one of the following statements is FALSE?

Consider a fully adiabatic piston-cylinder arrangement as shown in the figure. The piston is massless and cross-sectional area of the cylinder is 𝐴. The fluid inside the cylinder is air (considered as a perfect gas), with γ being the ratio of the specific heat at constant pressure to the specific heat at constant volume for air. The piston is initially located at a position 𝐿1. The initial pressure of the air inside the cylinder is 𝑃₁ ≫ 𝑃₀, where 𝑃₀ is the atmospheric pressure. The stop S₁ is instantaneously removed and the piston moves to the position 𝐿₂, where the
equilibrium pressure of air inside the cylinder is 𝑃₂ ≫ 𝑃₀.

What is the work done by the piston on the atmosphere during this process?

Consider a mixture of two ideal gases, X and Y, with molar masses M̅_X = 10 kg/kmol and M̅_Y = 20 kg/kmol, respectively, in a container. The total pressure in the container is 100 kPa, the total volume of the container is 10 m³ and the temperature of the contents of the container is 300 K. If the mass of gas-X in the container is 2 kg, then the mass of gas-Y in the container is ____ kg. (Rounded off to one decimal place)

Assume that the universal gas constant is 8314 J kmol^-1K^-1.