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Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
Calorimetry

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Calorimetry

Four 2 cm × 2 cm × 2 cm cubes of ice are removed from a...

Four 2 cm×2 cm×2 cm2 \text{ cm} \times 2 \text{ cm} \times 2 \text{ cm} cubes of ice are removed from a refrigerator and placed in 200 ml200 \text{ ml} of a drink at 10^{}^{{}^{\circ}} \text{C}. Determine the temperature of the drink once thermal equilibrium is reached. Assume that the container has negligible heat capacity and no heat is lost to the surroundings of the drink. Density of ice =900 kg m−3= 900 \text{ kg m}^{-3}, density of the drink =1000 kg m−3= 1000 \text{ kg m}^{-3}, specific heat capacity of the drink =4200 J kg−1 K−1= 4200 \text{ J kg}^{-1} \text{ K}^{-1}, and latent heat of fusion of ice =3.4×105 J kg−1= 3.4 \times 10^5 \text{ J kg}^{-1}.

Options

  1. A0^{}^{{}^{\circ}} \text{C}
  2. B-1.5^{}^{{}^{\circ}} \text{C}
  3. C2.5^{}^{{}^{\circ}} \text{C}
  4. D5.0^{}^{{}^{\circ}} \text{C}

Correct answer

A. 0^{}^{{}^{\circ}} \text{C}

Step-by-step solution

Volume of the four ice cubes is Vice=4×(2×2×2)=32 cm3=32×10−6 m3V_{\text{ice}} = 4 \times (2 \times 2 \times 2) = 32 \text{ cm}^3 = 32 \times 10^{-6} \text{ m}^3.

Mass of the ice is mice=Vice×ρice=32×10−6×900=0.0288 kgm_{\text{ice}} = V_{\text{ice}} \times \rho_{\text{ice}} = 32 \times 10^{-6} \times 900 = 0.0288 \text{ kg}.

Mass of the drink is mdrink=Vdrink×ρdrink=200×10−6×1000=0.2 kgm_{\text{drink}} = V_{\text{drink}} \times \rho_{\text{drink}} = 200 \times 10^{-6} \times 1000 = 0.2 \text{ kg}.

Assuming the initial temperature of the ice is 0^{}^{{}^{\circ}} \text{C}, the heat required to melt all the ice is Qreq=mice×L=0.0288×3.4×105=9792 JQ_{\text{req}} = m_{\text{ice}} \times L = 0.0288 \times 3.4 \times 10^5 = 9792 \text{ J}.

The maximum heat that can be released by the drink in cooling from 10^{}^{{}^{\circ}} \text{C} to 0^{}^{{}^{\circ}} \text{C} is Qrel=mdrink×cdrink×ΔT=0.2×4200×10=8400 JQ_{\text{rel}} = m_{\text{drink}} \times c_{\text{drink}} \times \Delta T = 0.2 \times 4200 \times 10 = 8400 \text{ J}.

Since Qrel<QreqQ_{\text{rel}} < Q_{\text{req}}, the heat released by the drink is insufficient to melt all the ice. Thus, only a fraction of the ice melts, and the mixture will consist of both ice and liquid.

Therefore, the system reaches thermal equilibrium at the melting point of ice, which is 0^{}^{{}^{\circ}} \text{C}.
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