By what amount must the temperature of 200cm3 3 of Nitrogen at 27°C be increased to double the pressure if the final volume is 150cm3 3 (Assume ideality)

By what amount must the temperature of 200cm${}^3$ of Nitrogen at 27°C be increased to double the pressure if the final volume is 150cm${}^3$ (Assume ideality)

Answer Details

Using the ideal gas law and equation:
$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$
$\frac{P_1\times 200{\text{cm}}^3}{300\text{K}}=\frac{2P\times 150{\text{cm}}^3}{T_2}$
Cross multiply:
$T_2=\frac{300\times 150\times 2P}{200\times P}$
$=450\text{K}$ or ${177}^{\circ }\text{C}$
Don't forget to convert to ${}^{\circ }\text{C}$