Answer to Question #116527 in Mechanics | Relativity for Augustine

Question #116527
A copper calorimeter of mass 150g was half-filled with water of mass 300g and temperature 0°C. 5g of ice at 0°C was added to the content, later some quantity of steam was passed into the mixture and the temperature rose by 20°C. Calculate the quantity of steam added? (Specific latent heat of vaporization of steam = 2260000j/kg, specific heat of copper = 400J/kg/K)
Expert's answer

Let us write the equation of thermodynamic equilibrium:

"c_cm_c\\Delta T + c_w(m_w+m_i)\\Delta T + m_i\\lambda_i = m_sL_s + m_sc_w\\Delta T_2" .

Here "L_s = 2260000\\,J\/kg, \\; c_c = 400\\,J\/kg\/K, \\;\\; c_w = 4200\\, J\/kg\/K, \\;\\; c_i = 2100\\; J\/kg\/K, \\;\\; \\lambda_i = 330000\\, J\/kg."

Next, we obtain the expression for the mass of steam

"m_s = \\dfrac{c_cm_c\\Delta T + c_w(m_w+m_i)\\Delta T + m_i\\lambda_i }{L_s + c_w\\Delta T_2} = \\\\\n= \\dfrac{400\\cdot0.150\\cdot20 + 4200\\cdot(0.3+0.005)\\cdot20 + 0.005\\cdot330000}{2260000 + 4200\\cdot80} \\approx 0.011\\,\\mathrm{kg}."

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