One litre of an ideal gas at a pressure of 5 bar expands isothermally into vacuum until its volume becomes 10 litres. What is the heat absorbed during this process? 

Under isothermal conditions, the internal energy of an ideal gas remains constant 
$\therefore ∆\mathrm{U} =0$
According to first law of thermodynamics 
$$\begin{gathered} ∆\mathrm{U} = \mathrm{q}+ \mathrm{w} \mathrm{w} = {\mathrm{p}}_{\mathrm{ext}} ({\mathrm{V}}_2-{\mathrm{V}}_1) \\ = 0 (10 -1 ) = 0\left(9\right) =0 \end{gathered}$$
No work is done: no heat is absorbed.