Question

What thermal volumetric contraction (expressed as a fraction of the original volume) of 1.7 kg of carbon disulfide releases enough energy to fully melt 1.7 kg of ice originally at 0 ?C? (Feel free to look up the relevant properties of these substances.)

Answer 1

Sol: Since melting of ice is an isothermal process (i.e. T = constant), from the 1st law of thermodynamics delta u = delta q - delta w therefore delta q = delta w Given: Mass of ice = 1.7 kg Mass of CS_2 = 1.7 kg properties of ice Latent heat of fusion = lambda = 333.55 KJ/kg properties of CS_2 Molecular wt. of CS_2 = 76.14 g/mol Moles of CS_2 = 1.7 times 10^-3/76.14 = 22.32 mol Now delta q = delta w q = rho p dv = rho^v_2_v_1 n RT/V dv [Assuming ideal gas p = nRT/V] q = -nRT ln (v_2/v_1) [-ve sign is due to contraction happening] We know that heat released by contraction is used to melt the ice therefore q = m lambda = -nRT ln v_2/v_1 1.7 times 333.55 times 10^3 = 22.32 times 8.314 times 273 ln (v_2/v_1 -11.19 =