The quality of heat absorbed by the gas, $\mathrm{Q}=\mathrm{\Delta }\mathrm{E}+\mathrm{W},$ here W is the work done by the gas. For free expansion i.e., expansion against vacuum, $\mathrm{W}=0$ ; at constant temperature , the internal energy of an ideal gas is constant and so $\mathrm{\Delta }\mathrm{E}=0$ . Thus $\mathrm{Q}=0$ .