Question

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 1

Given:

Mass of nitrogen gas, m = 2.0 × 10⁻² kg
Rise in temperature, ΔT = 45 °C = 45 K
Molecular mass of N₂ = 28 g mol⁻¹ = 0.028 kg mol⁻¹
Gas constant, R = 8.3 J mol⁻¹ K⁻¹

The gas is heated at constant pressure.

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Step 1: Calculate number of moles of nitrogen

n = m / M

n = (2.0 × 10⁻²) / 0.028

n = 0.714 mol

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Step 2: Write expression for heat supplied at constant pressure

Heat supplied:

Q = n C_p ΔT

For a diatomic gas (like N₂) at room temperature:

C_p = ⁷/₂ R

C_p = (7/2) × 8.3 = 29.05 J mol⁻¹ K⁻¹

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Step 3: Calculate the heat supplied

Q = 0.714 × 29.05 × 45

Q ≈ 9.33 × 10² J

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Final Answer:

The amount of heat required is
Q ≈ 9.3 × 10² J