A sample of air weighing 1.18 g occupies 1.0 × 103 cm3 when kept at 300 K and 1.0 × 105 Pa. When 2.0 cal of heat of added to it at constant volume, its temperature increases by 1°C. Calculate the amount of heat needed to increase the temperature of air by 1°C at constant to increase if the temperature of air by 1C at constant pressure if the mechanical equivalent of heat is 4.2 × 107 erg/cal. Assume that air behaves as an ideal gas.

Sol. m = 1.18 g, V = 1 × 10^3 cm^3 = 1 L T = 300 k, P = 10^5 Pa PV = nRT or n = PV/RT = 10^5 = atm. N = PV/RT = 1/8.2 * 10^-2 * 3 * 10^2 = 1/8.2 * 3 = 1/24.6 Now, C base v = 1/n = 24.6 * 2 = 49.2 C base p = R + C base v = 1.987 + 49.2 = 51.187 Q = nC base pdT = 1/24.6 * 51.187 * 1 = 2.08 Cal.

Sol. C base P/C base V = 7.6, n = 1 mole, ∆T = 50K (a) Keeping the pressure constant, dQ = du + dw, ∆T = 50 K, γ = 7/6, m = 1 mole, dQ = du + dw ⇒ nC base VdT = du + RdT ⇒ du = nCpdT – RdT = 1 * Rγ/γ – 1 * dT – RdT = R *7/6/7/6-1 dT – RdT = DT – RdT = 7RdT = 6 RdT = 6 * 8.3 * 50 = 2490 J. (b) Kipping Volume constant, dv = nC base VdT = 1 * R/γ – 1 * dT = 1 * 8.3/7/6-1 * 50 = 8.3 * 50 * 6 = 2490 J (c)Adiabetically dQ = 0, = [n * R/γ – 1(T base 1 – T base 2)] = 1 * 8.3/7/6 -1 (T base 1 – T base 2)] = 8.3 * 50 * 6 = 2490 J

Sol. . m = 1.18 g, V = 1 × 10^3 cm^3 = 1 L T = 300 k, P = 10^5 Pa PV = nRT or n = PV/RT = 10^5 = atm. N = PV/RT = 1/8.2 * 10^-2 * 3 * 10^2 = 1/8.2 * 3 = 1/24.6 Now, C base v = 1/n = 24.6 * 2 = 49.2 C base p = R + C base v = 1.987 + 49.2 = 51.187 Q = nC base pdT = 1/24.6 * 51.187 * 1 = 2.08 Cal.