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(B) Mass of nitrogen,$m = 2.0 	imes 10^{-2} \; kg = 20 \; g$.Rise in temperature,$\Delta T = 45 \; ^{\circ}C$.Molecular mass of $N_{2}$,$M = 28 \; g/

Vedclass · Accepted Answer

$933$

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(B) Mass of nitrogen,$m = 2.0 	imes 10^{-2} \; kg = 20 \; g$.Rise in temperature,$\Delta T = 45 \; ^{\circ}C$.Molecular mass of $N_{2}$,$M = 28 \; g/mol$.Universal gas constant,$R = 8.3 \; J \; mol^{-1} K^{-1}$.Number of moles,$n = \frac{m}{M} = \frac{20}{28} = \frac{5}{7} \; mol$.For a diatomic gas like nitrogen,the molar specific heat at constant pressure is $C_{p} = \frac{7}{2} R$.$C_{p} = \frac{7}{2} 	imes 8.3 = 29.05 \; J \; mol^{-1} K^{-1}$.The total amount of heat supplied at constant pressure is given by $\Delta Q = n C_{p} \Delta T$.$\Delta Q = \left( \frac{5}{7} ight) 	imes 29.05 	imes 45$.$\Delta Q = \frac{5}{7} 	imes \left( \frac{7}{2} 	imes 8.3 ight) 	imes 45 = \frac{5}{2} 	imes 8.3 	imes 45$.$\Delta Q = 2.5 	imes 373.5 = 933.75 \; J$.Rounding to the nearest integer,the heat supplied is $933 \; J$.

What amount of heat (in $J$) 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 $N_{2} = 28; R = 8.3 \; J \; mol^{-1} K^{-1}$.)

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