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How many milliliters of water at 23 °C with a density of 1.00 g/mL must be mixed with 180 mL (about 6 oz) of coffee at 95 °C so that the resulting combination will have a temperature of 60 °C? Assume that coffee and water have the same density and the same specific heat.

Respuesta :

Answer:

V H2O = 170.270 mL

Explanation:

  • QH2O ( heat gained) = Qcoffe ( heat ceded)

⇒ Q = mCΔT

∴ m: mass (g)

∴ C: specific heat

assuming:

  • δ H2O = δ Coffe = 1.00 g/mL
  • C H2O = C coffe = 4.186 J/°C.g....from literature

⇒ Q coffe = (mcoffe)(C coffe)(60 - 95)

∴ m coffe = (180mL)(1.00 g/mL) = 180 g coffe

⇒ Q  = (180g)(4.186 J/°C.g)(-35°C) = - 26371.8 J

⇒ Q H2O = 26371.8 J = (m)(4.186 J/°C.g)(60 - 23)

⇒ (26371.8 J)/(154.882 J/g) = m H2O

⇒ m H2O = 170.270 g

⇒ V H2O = (170.270 g)(mL/1.00g) = 170.270 mL

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