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 N2 = 28; R = 8.3 J mol–1 K–1.)
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Answer 1

$\huge \bold{answer}$

Mass of nitrogen, m = 2.0 × 10–2 kg = 20 g

Rise 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 = m/M

= (2 × 10-2 × 103) / 28

= 0.714

Molar specific heat at constant pressure for nitrogen, Cp = (7/2)R

= (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 = nCP ΔT

= 0.714 × 29.05 × 45

= 933.38 J

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

Answer 2

★ Given:-

The Molecular mass of Nitrogen, M = 28

Universal gas Constant, R = 8.3 J mol-¹ K-¹

Mass of Nitrogen, m = 1.8 × 10-² kg = 18 g

Now, the number of moles, n =

$\frac{mass \: of \:N_{2} }{Molecular \: mass \: of \: N_{2}} = \frac{m}{M} = \frac{18}{28}$

Therefore, n = 0.643

Now, for Nitrogen Molar specific heat at constant pressure,

$C_{p} = \frac{7}{2}$

$R = \frac{7}{2} \times 8.3$

Therefore, Cp = 29.05 J mol-¹ K-¹

Now, the total amount of heat that is to be supplied to increase its temperature by 50 °C:

→ ∆Q = n × Cp × ∆T

$\implies \Delta Q = 0.643 \times 29.05 \times 50 = 933.9575J$

Therefore, the total amount of heat that is to be supplied to raise the temperature of Nitrogen by 50 °C = 933.9575 J.