An ideal gas is contained in a cylinder by means of a movable frictionless piston, as illustrated in [Figure 2.1]. Initially, the gas has a volume of 1.8 × 10^-3 m³ at a pressure of 3.3 × 10^5 Pa and a temperature of 310 K.

1. (a)Show that the number of gas molecules in the cylinder is 1.4 × 10^23.[2]
2. (b)Use kinetic theory to explain why, when the piston is moved so that the gas expands, this causes a decrease in the temperature of the gas.[3]
3. (c)The gas expands so that its volume increases to 2.4 × 10^-3 m³ at a pressure of 2.3 × 10^5 Pa and a temperature of 288 K, as shown in [Figure 2.2].
4. (c)(i)The average translational kinetic energy EK of a molecule of an ideal gas is given by EK = (3/2)kT where k is the Boltzmann constant and T is the thermodynamic temperature. Calculate the increase in internal energy ΔU of the gas during the expansion. ΔU = .............................................................. J [3][3]
5. (c)(ii)The work done by the gas during the expansion is 76 J. Use your answer in (i) to explain whether thermal energy is transferred to or from the gas during the expansion.[2]

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