A calorimeter of mass 50 g and specific heat capacity $0.42 J . g^{- 1} . {}^{\circ}C^{- 1}$ contains some mass of water at $20^{\circ} C$ . A metal piece of mass 20 g at $100^{\circ} C$ is dropped into the calorimeter. After stirring, the final temperature of the mixture is found to be $22^{\circ} C$ .Find the mass of water used in calorimeter.
(Take, specific heat capacity of metal piece = $0.3 J . g^{- 1} . {}^{\circ}C^{- 1}$ and specific heat capacity of water = $0.42 J . g^{- 1} . {}^{\circ}C^{- 1}$ )

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Solution

Step 1: Given data
Mass of calorimeter $m = 50 g$
Mass of the metal piece $m' = 20 g$
Specific heat capacity of the calorimeter $c = 0.42 J . g^{- 1} . {}^{\circ}C^{- 1}$
Highest temperature $T' = 100^{\circ} C$
Final temperature $T = 22^{\circ} C$
Lowest temperature $T'' = 20^{\circ} C$
Specific heat capacity of the metal piece $c' = 0.3 J . g^{- 1} . {}^{\circ}C^{- 1}$
Specific heat capacity of water $c'' = 0.42 J . g^{- 1} . {}^{\circ}C^{- 1}$
Step 2: Finding heat lost
$Heat lost by the metal piece = m' c' (T' - T) Q' = 20 g \times 0.3 J . g^{- 1} . {}^{\circ}C^{- 1} \times (100^{\circ} C - 22^{\circ} C) Q' = 468 J$
Step 3: Finding heat gained by the water
$Heat gained by water = m'' c'' (T - T'') Q = m'' \times 0.42 J . g^{- 1} . {}^{\circ}C^{- 1} \times (22^{\circ} C - 2^{\circ} C) Q = 8.4 m'' J$
Step 4: Finding heat gained by the calorimeter
$Heat gained by calorimeter = m c (T - T'') Q'' = 50 g \times 0.42 J . g^{- 1} . {}^{\circ}C^{- 1} \times (22^{\circ} C - 20^{\circ} C) Q'' = 42 J$
Step 5: Finding the mass of the water
$Heat lost = Heat the gained 468 J = 8.4 m'' J + 42 J 426 = 8.4 m'' m'' = 50.71 g$
Thus the mass of the water is 50.71 g.

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Q. A calorimeter of mass

50 g

and specific heat capacity

0.42 J g^{- 1} ℃^{- 1}

contains some mass of water at

20^{o} C

. A metal piece of mass

20 g

100^{o} C

is dropped into the calorimeter. After stirring, the final temperature of the mixture is found to be

22^{o} C

. Find the mass of water used in the calorimeter.
[specific heat capacity of the metal piece

= 0.3 J g^{- 1} ℃^{- 1}

specific heat capacity of water

= 4.2 J g^{- 1} ℃^{- 1}

]

A calorimeter of mass $50 g$ specific heat capacity $0.42 J g^{- 1} {}^{o}{C^{- 1}}$ contains some mass of water at $20^{o} C$ . A metal piece of mass $20 g$ at $100^{o} C$ is dropped into the calorimeter. After stirring, the final temperature of the mixture is found to be $22^{o} C$ . Find the mass of water used in the calorimeter. (Take specific heat capacity of the metal piece $0.3 J g^{- 1} {}^{o}{C^{- 1}}$ , specific heat capacity of water $4.2 J g^{- 1} {}^{o}{C^{- 1}}$ )

Q. A metal object weighing

25^{\circ} C

is dropped in a calorimeter of mass

80

g and specific heat capacity of

1 J {k g}^{- 1} K^{- 1}

, containing 100 g of water at

40^{\circ} C

. final temperature recorded was

35^{\circ} C

. find the specific heat capacity of metal object.
specific heat capacity of water

4200 J {k g}^{- 1} K^{- 1}

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