Describe how the ideal gas constant R is defined.

Calculate the temperature of 0.100 mol of an ideal gas kept in a cylinder of volume 1.40×10^–3 m³ at a pressure of 2.32×10⁵ Pa.

The gas in (b) is kept in the cylinder by a freely moving piston. The gas is now heated at constant pressure until the volume occupied by the gas is 3.60×10^–3 m³. The increase in internal energy of the gas is 760 J. Determine the thermal energy given to the gas.

After heating, the gas is compressed rapidly to its original volume in (b). Outline why this compression approximates to an adiabatic change of state of the gas.

defined from the equation of state of an ideal gas PV=nRT;
all symbols (PVnT) correctly identified;

390/391 K;

work done\( = \left( {P\Delta V = 2.32 \times {{10}^5} \times 2.20 \times {{10}^{ - 3}} = } \right)510{\rm{J}}\);
thermal energy\( = \left( {760 + 510 = } \right)1.27 \times {10^3}{\rm{J}}\);
Award [1 max] if volume is taken as 3.6×10^–3, giving an answer of 1600 J.

an adiabatic change is one in which no (thermal/heat) energy is transferred between system and surroundings / no energy enters/leaves system;
a rapid compression means that there is insufficient time (for energy transfer) / OWTTE;