Open Physics Challenge:
One mole of a gas is put under weightless piston of a vertical cylinder at temprature T.the space over opens into atmosphere.Initially piston was in equilibrium.How much work should be odn by some external force to increase isothermally the volume under piston twice the volume?

Question

Open Physics Challenge:
One mole of a gas is put under weightless piston of a vertical cylinder at temprature T.the space over opens into atmosphere.Initially piston was in equilibrium.How much work should be odn by some external force to increase isothermally the volume under piston twice the volume?

nikvist · Answer

$$pV=n_mRT\quad,\quad p=n_mRT\frac{1}{V}$$$$A=\int pdV=n_mRT\int\limits_{V_0}^{2V_0}\frac{dV}{V}=n_mRT\cdot\ln{2}\quad(n_m=1mol)$$

anonymous · Answer

no
try to find out what you missed

anonymous · Answer

Ans is 
$$n_mRT(1-\ln2)$$
You ignored work done against atmosphere

anonymous · Answer

Get it

nikvist · Answer

$$p_0V_0=pV=n_mRT$$$$A=\int(p_0-p)dV=\int p_0dV-\int pdV=$$$$=p_0\int\limits_{V_0}^{2V_0}dV-n_mRT\int\limits_{V_0}^{2V_0}\frac{dV}{V}=p_0V_0-n_mRT\cdot\ln{2}=$$$$=n_mRT(1-\ln{2})$$Now is OK