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 N_{2} = 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 = nC_{P}ΔT

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

Here the Substance is Nitrogen Gas (N_{2}) , 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 ^{o}C or K , both have same interpretation)

To find the moles of N_{2} 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 N_{2} as

m = 2.0 × 10^{–2} kg

1 Kg = 1000 g , so we have

m = 2.0 × 10^{–2} × 10^{3} = 20 g

molar mass of N_{2} gas is

M = 28 g/mol

So the number of moles of N_{2} gas is

so putting the value of ΔT,n,C_{P} in the equation ΔQ = nC_{P}ΔT

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 45^{o}C at constant Pressure

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