Question

What amount of heat must be supplied to \(2.0 \times 10^{−2}~ 𝑘𝑔\) of nitrogen (at room temperature) to raise its temperature by \(45^{\circ}𝐶\) at constant pressure? (Molecular mass of \(𝑁_{2}=28; 𝑅 = 8.3~ 𝐽~ 𝑚𝑜𝑙^{−1} 𝐾^{−1}.\))

Answer 1

Given,

Mass of nitrogen \((𝑚)= 2 \times 10^{−2}~ 𝑘𝑔 = 20~𝑔\)

Rise in temperature \((\bigtriangleup 𝑇)=45^{\circ}𝐶\)

Molecular mass of \(N_{2}, 𝑀=28\)

Universal gas constant, \(𝑅=8.3~ 𝐽~𝑚𝑜𝑙^{−1} 𝑘^{−1}\)

Number of moles of \(𝑁_{2}\)

\( 𝑛=\dfrac{𝑚}{𝑀}=\dfrac{20}{28}=0.714~ 𝑚𝑜𝑙\)

Molar specific heat at constant pressure for \(N_{2}:\)

\( 𝐶_{𝑃}=\dfrac{7𝑅}{2}\)

Putting the value of \(R\)

\(𝐶_{𝑃}=\dfrac{7 \times 8.3}{2}=29.05~ 𝐽~𝑚𝑜𝑙^{−1} 𝑘^{−1}\)

Total amount of heat supplied will be,

\(\bigtriangleup 𝑄=𝑛𝐶_{𝑃} \bigtriangleup 𝑇\)

\( =0.714 \times 29.05 \times 45\)

\( =933.38~ 𝐽\)