Answer to Question #124120 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

Let the initial volume of the gas $V_i=V$

Final volume of the gas$V_f=2V$

initial pressure of the gas$P_i=P$

final pressure of the gas $P_f=2P$

Initial temperature of the gas $T_i=0+273=273k$

Final temperature of the gas $T_f=?$

total number of mole of the gas is not getting change hence,

Using the ideal gas equation, total number of moles of the gas $n=\frac{PV}{RT}$

Hence,

$\frac{P_iV_i}{T_i}=\frac{P_fV_f}{T_f}$

Now, equating both side,

$\Rightarrow T_f=\frac{P_fV_fT_i}{P_iV_i}$

Now, substituting the values,

$\Rightarrow T_f=\frac{2P\times 2V\times 273k}{PV}$

$\Rightarrow T_f=4\times 273k=1092k$

$\Rightarrow T_f=1029-273=756^\circ C$