Q. 15.0( 1 Vote )

# 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?

Given

Initial temperature of water T1=15 =288K

Final temperature of water T2=17 =290K

Specific heat capacity of copper cc=420 J kg–1 K–1

Specific heat capacity of water cw=4200 J kg–1 K–1

Mass of copper vessel mc=100g = 100×10-3kg

Mass of water mw=200g = 200×10-3kg

a) It is given that copper vessel is thermally insulated. Therefore, no heat from the surroundings can be transferred to the liquid-vessel system.

b) Work done on this system will be

ΔW=mwcwΔT + mcccΔT

ΔT=T2-T1=290-288=2K

So,

ΔW= 200×10-3×4200×2 + 100×10-3×420×2

ΔW=1680 + 84=1764J

work done on the system is 1764J.

c) From first law of thermodynamics, we know that,

ΔQ=ΔU+ΔW

Where ΔQ=heat supplied to the system

ΔU=change in internal energy

ΔW=work done by the system

From part (a) we have concluded that ΔQ=0

So, first law becomes

ΔU=-ΔW

Work done on the system ΔW=1764 J

So, work done by the system ΔW=-1764J

ΔU = -(-1764) = 1764J

Increase in internal energy of the system = 1764J.

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