In a vertically located cylinder under a heavy piston there is m = 14 g of nitrogen. How much heat does the gas

In a vertically located cylinder under a heavy piston there is m = 14 g of nitrogen. How much heat does the gas receive when it is heated from t1 = 25∘ to t2 = 225∘C? Express the answer in kJ, rounded to tenths. Molar mass of nitrogen μ = 28 g / mol, universal gas constant R = 8.31 J / (mol⋅K)

m = 14 g = 0.014 kg.

T1 = 298 “K.

T2 = 498 “K.

μ = 28 g / mol = 0.028 kg / mol.

R = 8.31 J / (mol * K).

Q -?

According to 1 law of thermodynamics: Q = ΔU + A. Since the gas does not perform work A = 0, then the entire amount of heat Q goes to increase the internal energy of the gas ΔU.

Q = ΔU.

The change in the internal energy of a monatomic gas ΔU is determined by the formula: ΔU = 3 * m * R * ΔТ / 2 * μ.

Q = 3 * m * R * ΔТ / 2 * μ.

Q = 3 * 0.014 kg * 8.31 J / (mol * K) * (498 “K – 298” K) / 2 * 0.028 kg / mol = 1246.5 J = 1.3 kJ.

Answer: the gas received Q = 1.3 kJ of thermal energy.