# A 500 m3 balloon is filled with helium under a pressure of 0.8 * 10 ^ 5 Pa. As a result of solar heating

**A 500 m3 balloon is filled with helium under a pressure of 0.8 * 10 ^ 5 Pa. As a result of solar heating, the temperature of the gas in the ball rose from 12 ° C to 27 ° C. Determine the change in the internal energy of the gas.**

From the Mendeleev – Clapeyron equation p ∙ V = ν ∙ R ∙ T we express ν ∙ R = (p ∙ V) / Т. Knowing that a balloon with a volume of V = 500 m ^ 3 is filled with helium under a pressure of p = 0.8 ∙ 10 ^ 5 Pa at a gas temperature in the balloon T = 12 ° C = 12 + 273 K = 285 K, substituting the values of physical quantities, we get: ν ∙ R = (0.8 ∙ 10 ^ 5 ∙ 500) / 285 = 1.4 ∙ 10 ^ 5 (J / K). The change in the internal energy of the gas is determined by the formula: ΔU = 1.5 ∙ ν ∙ R ∙ ΔT, where ν is the number of gas moles, R = 8.31 J / (mol ∙ K) is the universal gas constant, ΔT is the temperature change. According to the condition of the problem, as a result of solar heating, the gas temperature in the ball rose from 12 ° C to 27 ° C, that is, ΔT = 27 – 12 = 15 (K). Then ΔU = 1.5 ∙ 1.4 ∙ 10 ^ 5 ∙ 15 = 31.5 ∙ 10 ^ 5 J = 3.15 MJ. Answer: 3.15 MJ is the change in the internal energy of the gas.