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Units and Dimensions

A 50 g sample...

Question

A 50 g sample of metal was heated to $100^{0} C$ and then dropped into a beaker containing $50 g$ of water at $25^{0} C$ . If the specific heat capacity of the metal is 0.25 cal/g, what is the final temperature of the water in $^{0} C$ ?

A

27

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B

40

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C

60

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D

86

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Solution

The correct option is B 40
$[m C (T f - T i)]_{m e t a l} + [m C (T f - T i)]_{w a t e r} = 0$
Which can then become:
$[m C (T_{i} - T_{f})]_{m e t a l} = [m C (T_{f} - T_{i})]_{w a t e r}$
$50 \times 0.25 (100 - T_{f}) = 50 \times 4.184 (T_{f} - 25)$
$12.5 (100 - T_{f}) = 209.2 (T_{f} - 25)$
$1250 - 12.5 T_{f} = 209.2 T_{f} - 5230$
$1250 + 5230 = 209.2 T_{f} + 12.5 T_{f}$
$6480 = 221.7 T_{f}$
$T_{f} = \frac{6480}{221.7} = 29^{o} C$

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