A hot air balloon has volume of $$2000 \mathrm{~dm}^3$$ at $$99^{\circ} \mathrm{C}$$. What is the new volume if air in balloon cools to $$80^{\circ} \mathrm{C}$$ ?

If $$\mathrm{N}_2$$ gas is compressed at 2 atmosphere from 9.0 L to $$3.0 \mathrm{~L}$$ at $$300 \mathrm{~K}$$, find the final pressure at same temperature.

What is the volume in $$\mathrm{dm}^3$$ occupied by $$3 \mathrm{~mol}$$ of ammonia gas at STP?

Which of the following formulae is used to determine compressibility factor for measurement of deviation from ideal behaviour?