Question:

What amount of heat must be supplied to 2.0×1022.0 × 10^–2 kg of nitrogen (at room temperature) to raise its temperature by 45 °C at constant pressure ? (Molecular mass of N2N_2 = 28; R = 8.3 J mol1K1mol^{–1} K^{–1}.)

Updated On: Nov 2, 2023
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Solution and Explanation

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=mMn=\frac{m}{M}

=2.0×102×10328=0.714=\frac{2.0×10^{-2}×10^3}{28}=0.714

Molar specific heat at constant pressure for nitrogen,  cp=72Rc_p=\frac{7}{2}\,R

=72×8.3=\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=CpnΔTΔQ = C_p^n ΔT

=0.714×29.05×45= 0.714 × 29.05 × 45

=933.38J = 933.38 \,J

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

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