Q. 24.3( 13 Votes )

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 N2 = 28; R = 8.3 J mol–1 K–1.)

Answer :

we know amount of heat transferred to any substance (solid , liquid, Gas) at constant pressure is given by the relation


ΔQ = nCPΔT


Where ΔQ is the amount of heat supplied to the substance in raising it temperature by ΔT, CP is the molar specific heat of substance at constant pressure, n is the number of moles of substance.


Here the Substance is Nitrogen Gas (N2) , which is a diatomic gas, for a diatomic Gas the molar specific heat is



R is universal Gas Constant , R = 8.3 J mol–1 K–1


The rise in temperature is of 45°C, so we have


ΔT = 45°C = 45 K


(since we are only concerned with difference of temperature so unit can be either oC or K , both have same interpretation)


To find the moles of N2 Gas we have the relation


n = m/M


where n is the number of moles of gas, m is the mass of gas in grams (g) and M is the Molar mass of the gas in g/mol


here we are given mass of N2 as


m = 2.0 × 10–2 kg


1 Kg = 1000 g , so we have


m = 2.0 × 10–2 × 103 = 20 g


molar mass of N2 gas is


M = 28 g/mol


So the number of moles of N2 gas is



so putting the value of ΔT,n,CP in the equation ΔQ = nCPΔT


ΔQ = 0.714mol ×(7/2) × R × 45 K


= 0.714mol × 3.5 × 8.3 J mol–1 K–1 × 45K


= 933.38 J


So 933.38 J heat must be supplied to 20g nitrogen gas to raise its temperature by 45oC at constant Pressure


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