Water at 15^ ^ ^ C is contained inside a closed, thermally insulated copper vessel. The temperature increases to 17^ ^ ^ C after the vessel is vigorously shaken for 15 minutes. The mass of the water is 200 g and the

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Correct answer: D. 1764 J

According to the first law of thermodynamics,

\Delta U = Q + W

.

Since the vessel is thermally insulated,

Q = 0

, which gives

W = \Delta U

.

The change in internal energy of the system is the sum of the changes in internal energy of the water and the copper vessel:

\Delta U = m_w c_w \Delta T + m_c c_c \Delta T

Substituting the given values:

m_w = 0.2 \text{ kg}

,

c_w = 4200 \text{ J kg}^{-1} \text{ K}^{-1}

m_c = 0.1 \text{ kg}

,

c_c = 420 \text{ J kg}^{-1} \text{ K}^{-1}

\Delta T = 17^{{}^{{}^{\circ}}}\text{C} - 15^{{}^{{}^{\circ}}}\text{C} = 2 \text{ K}

W = (0.2 \times 4200 + 0.1 \times 420) \times 2

W = (840 + 42) \times 2

W = 882 \times 2 = 1764 \text{ J}

Water at 15^ ^ ^ C is contained inside a closed, thermally...

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