# What Amount of Heat Must Be Supplied to 2.0 X 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.) - Physics

What amount of heat must be supplied to 2.0 x 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.)

#### Solution 1

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

Rise in temperature, ΔT = 45°C

Molecular mass of N2M = 28

Universal gas constant, R = 8.3 J mol–1 K–1

Number of moles, n = m/M

= (2.0xx10^(-2)xx10^3)/28 = 0.714

Molar specific heat at constant pressure for nitrogen, C_P = 7/2 R

= 7/2 xx 8.3

= 29.05 J mol^(-1) K^(-1)

The total amount of heat to be supplied is given by the relation:

ΔQ = nCΔT

= 0.714 × 29.05 × 45

= 933.38 J

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

#### Solution 2

Here, mass of gas, m= 2xx 10^-2 kg = 20 g

rise in temperature, triangleT = 45 ^@C

Heat required, triangleQ = ?, Molecular mass, M = 28

Number of moles , n = m/M = 20/28 = 0.714

As nitrogen is a diatomatic gas,molar specific heat at constant pressure is

C_p = 7/2R = 7/2 xx 8.3 J mol^(-1) K^(-1)

As triangleQ = nC_p triangleT

:. triangleQ = 0.714 xx 7/2 xx 8.3 xx 45 J = 933.4 J

Is there an error in this question or solution?

#### APPEARS IN

NCERT Class 11 Physics Textbook
Chapter 12 Thermodynamics
Q 2 | Page 316
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