Using both kinetic energy and potential energy, explain the meaning of the internal energy of an ideal gas.
A fixed mass of ideal gas at $20^{\circ}\text{C}$ is trapped in a cylinder by a piston, as shown in Fig. 2.1. The gas initially occupies a volume of $1.24 \times 10^{-4}\,\text{m}^3$. Thermal energy is added to the gas and its volume rises by $5.20 \times 10^{-5}\,\text{m}^3$.
The piston can move freely, so the gas always remains at atmospheric pressure. Atmospheric pressure is $1.01 \times 10^{5}\,\text{Pa}$. Calculate the work done by the gas.
Calculate the final thermodynamic temperature $T$ of the gas.
The gas has a mass of $16\,\text{g}$. During this expansion, a net $960\,\text{J}$ of thermal energy is transferred to the gas. Calculate the specific heat capacity $c$ of the gas at this pressure.
The gas in (b) is allowed to return to its original temperature. The piston is then locked in place. Thermal energy is supplied until the temperature reaches the same final value as in (b). Use the first law of thermodynamics to suggest and explain how the specific heat capacity of the gas in this situation compares with the value in (b)(iii).