200 ,g of ice at -20^{circ} C is mixed with 500 ,g of water at 20^{circ} C in an insulating vessel.

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10-1.Thermometry, Thermal Expansion and Calorimetry

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$200 \,g$ of ice at $-20^{\circ} C$ is mixed with $500 \,g$ of water at $20^{\circ} C$ in an insulating vessel. Final mass of water in vessel is ........... $g$ (specific heat of ice $=0.5 \,cal g ^{-10} C ^{-1}$ )

A

$700$

B

$600$

C

$400$

D

$200$

Solution

(b)

Maximum heat supplied by water

$\Delta Q_1=500 \times 1 \times(20-0)$

$=10,000 \,cal$

Heat required to raise the temperature of ice upto $0^{\circ} C$

$\Delta Q_2=200 \times 0.5 \times 20$

$=2000 \,cal$

$\Delta Q_1-\Delta Q_2=8000 \,cal$

Melts the ice

$8000=m \times 80$

$m=100 \,g$

So, mass of water is $500+100=600 \,g$.

Standard 11

Physics

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(JEE MAIN-2022)