A glass vessel contains air at 60⁰C. To what temperature must it be heated to expel one third of the air, the pressure remaining constant. (Neglect the expansion of the vessel)

Here pressure and volume both are constant only mass and temperature are changing.

$\mathrm{mass} \mathrm{of} \mathrm{a} \mathrm{gas} \mathrm{in} \mathrm{inversely} \mathrm{proportional} \mathrm{to} \mathrm{absolute} \mathrm{temperature}$

$\mathrm{If} \mathrm{one} \mathrm{third} \mathrm{mass} \mathrm{of} \mathrm{the} \mathrm{gas} \mathrm{has} \mathrm{expelled}$

$\mathrm{remaining} \mathrm{gas} \mathrm{is} \mathrm{two} \mathrm{third}$

$Hence m_2=\frac{2m_1}{3}$

$\frac{{\mathrm{m}}_1}{{\mathrm{m}}_2}=\frac{{\mathrm{T}}_2}{{\mathrm{T}}_1}$

$\frac{{\mathrm{m}}_{1}3}{2{\mathrm{m}}_1}=\frac{{\mathrm{T}}_2}{273+60}=\frac{{\mathrm{T}}_2}{333}$

${\mathrm{T}}_2=499.5\mathrm{K}$

$t_2=499.5-273=226.5^{0}C$