Answer to Question #124076 in Classical Mechanics for ABIOJE OLUWAPELUMI

Question

To what temperature must a given mass of nitrogen at 0⁰c be heated so that both its volume and pressure will be doubled?

Answer 1

Assuming number of molecules are constant let us consider at temperature $T_1=273K$

Pressure and volume are $P_1,V_1$ respectively and at temperature $T_2$ , given that pressure and volume are $P_2=2P_1,V_2=2V_1$ respectively.

Thus, from ideal gas law we get,

$$PV\propto T\\ \implies \frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\\ \implies T_2=4T_1=1092K=819^{\circ}C$$