An ideal gas within a closed system undergoes an isothermal expansion from an initial volume of 1m^3 to 2m^3. Given that the initial pressure of the gas is 10^5 Pa, find the final pressure of the gas following the expansion.

The key word to note in this question is that the expansion is isothermal and that we have a closed system. This means that the expansion must happen at a constant temperature (isothermal), and that the number of particles doesn't change (closed system). For an ideal gas, we can write PV = NKT, however here we know that N (number of particles), K (Boltzmann's constant) and T (temperature) are all constant, and therefore PV = constant. This is known as Boyle's Law. In words, the product of pressure and volume must be constant at all times. This must therefore be true at the beginning and end of the expansion of the ideal gas, and so we can write P_iV_i = constant = P_fV_f , where the subscript i denotes the initial values and subscript f denotes the final values. We are after the final pressure P_f, and so by dividing both sides of the above equation by V_f, we get thatP_f = (P_iV_i )/V_f = (10⁵Pa X 1 m³)/2 m³ = 5 x 10⁴ Pa. So the total pressure of the gas has halved due to the volume doubling.