1. Ideal gases follow the equation,PV = NkBTHere, N is the number of molecules of a gas and kB = 1.38 × 10−23 JK−1(joule per kelvin) iscalled the Boltzmann constant, with P, V, T being the pressure,...

1. Ideal gases follow the equation,PV = NkBTHere, N is the number of molecules of a gas and kB = 1.38 × 10−23 JK−1(joule per kelvin) iscalled the Boltzmann constant, with P, V, T being the pressure, volume and temperature,respectively. Suppose you are given 23.6 liter of a gas. It is cooled down to a temperature of 0°Celsius and you find that the gas is at a pressure of 1 atmosphere. How many molecules of gas arethere in the container? (Be very careful in converting units and taking everything in SI units,especially the temperature. The units of kB should give you a clue.)

2. If the temperature of a gas is not kept constant, Boyle’s law changes to the form

P1V1γ = P2V2γThis is called adiabatic (or sudden) expansion. This happens when the gas is suddenly expanded,so the gas does not get enough time to exchange heat with the surroundings, so it absorbs heatfrom itself. Suppose, the pressure of a gas is doubled, and we see that its volume becomes 1/8 ofits original volume. What is the value of γ? (Assume same initial pressure and volume for the gas, you will see that the answer does not depend on your initial assumption.)