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.