A closed bottle contains some liquid. the bottle is shaken vigorously for 5 minutes. It is found that the temperature of the liquid is increased. Is heat transferred to the liquid? Is work done on the liquid? Neglect expansion on heating.

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Solution

A closed bottle containing some liquid is shaken vigorously such that work is done on the bottle (against the viscous force). Hence, the temperature of the liquid increases. However, no external heat is supplied to the system.

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Q. A thermally insulated, closed copper vessel contains water at

15^{0} C

. When the vessel is shaken vigorously for

15

minutes, the temperature rises to

17^{0} C

. The mass of the vessel is

100 g

and that of the water is

200 g

. The specific heat capacities of copper and water are

{420 J kg}^{- 1} K^{- 1}

and

{4200 J kg}^{- 1} K^{- 1}

respectively. Neglect any thermal expansion.
(a) How much heat is transferred to the liquid-vessel system?
(b) How much work has been done on this system?
(c) How much is the increase in internal energy of the system?

Q. A thermally insulated, closed copper vessel contains water at 15°C. When the vessel is shaken vigorously for 15 minutes, the temperature rises to 17°C. The mass of the vessel is 100 g and that of the water is 200 g. The specific heat capacities of copper and water are 420 J kg⁻¹ K⁻¹ and 4200 J kg⁻¹ K⁻¹ respectively. Neglect any thermal expansion. (a) How much heat is transferred to the liquid-vessel system? (b) How much work has been done on this system? (c) How much is the increase in internal energy of the system?

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