1. A Cylinder X, with an inner volume of 0.1 m³ contains hydrogen at 300 K and 5 x 105 Pa pressure. Itis connected with cylinder Y by a narrow tube with a tap as shown in Figure 10. The tap is initially closed. Cylinder Y has four times the inner volume of cylinder X and contains the same gas at the same temperature with a pressure of 2 × 10° Pa. The molar mass of hydrogen is 2 g mol-1. (a) Calculate the r.m.s speed of the hydrogen gas molecules in cylinder X. (b) Calculate the total internal energy of the gas in cylinder X. (c) The tap between X and Y is opened and the gas in the two cylinders mix. The temperature of the gases remains 300 K . Explain why this is so. (d) Calculate the resulting pressure of the mixture. (e) (Do this question at the end.) Suppose the gas in cylinder X was at a temperature of 600 K and pressure 2 x 10° Pa and the gas in cylinder Y was at a temperature of 300 K and the same pressure2 x 105 Pa before the valve was opened. What would be the final temperature when the gases mix after the valve is opened?

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