Question

What amount of heat must be supplied to $2.0 × 10^–2$ kg of nitrogen (at room temperature) to raise its temperature by 45 °C at constant pressure ? (Molecular mass of $N_2$ = 28; R = 8.3 J $mol^{–1} K^{–1}$.)

Answer 1

Mass of nitrogen, m = 2.0 × 10-2 kg=20 g

in temperature, ΔT = 45°C

Molecular mass of N2, M = 28

Universal gas constant, R = 8.3 J mol-1 k-1

Number of moles, $n=\frac{m}{M}$

$=\frac{2.0×10^{-2}×10^3}{28}=0.714$

Molar specific heat at constant pressure for nitrogen, $c_p=\frac{7}{2}\,R$

$=\frac{7}{2}×8.3$

=29.05 J mol-1 K-1

The total amount of heat to be supplied is given by the relation:

$ΔQ = C_p^n ΔT$

$= 0.714 × 29.05 × 45$

$= 933.38 \,J$

Therefore, the amount of heat to be supplied is 933.38 J.