Question

A 2.00-mol sample of helium gas initially at 300K and 0.400 atm is compressed isothermally to 1.20 atm. Noting that the helium behaves as an ideal gas, find
(a) the final volume of the gas
(b) the work done on the gas, hence, find the energy transffered by heat.

Answer 1

1. For an isothermic process we have $T=const$ and thus $P_f V_f = \nu R T$ , as helium is considered to be an ideal gas. Thus $V_f = \frac{2\cdot 8.31 \cdot 300}{1.2 \cdot 10^5}=41.55 \cdot 10^{-3}m^3=41.55l$.
2. The work done on the gas is given by $A=-\int PdV$. As in a isothermic process $PV=\nu RT=const$, we find $A=-\nu R T\ln(\frac{P_i}{P_f})\approx 5480 J = 5.48kJ$. As the process is isothermic, the change of internal energy is zero and thus $Q=A=5.48kJ$ transferred to the gas.