In an experiment, a sphere of aluminium of mass 0 . 20kg is heated...

In an experiment, a sphere of aluminium of mass

0 . 20kg

is heated up to

150 ° C

. Immediately, it is put into water of volume

150cc

{27}^{o}C

kept in a calorimeter of water equivalent to

0 . 025kg

. The final temperature of the system is

{40}^{o}C

. The specific heat of the aluminium is(take

4 . 2Joule = 1calorie

)

Options

A $434{\text{J kg}}^{- 1}{}^{o}C$
B $378{\text{J kg}}^{- 1}\text{°}C$
C $315{\text{J kg}}^{- 1}{}^{o}C$
D $476{\text{J kg}}^{- 1}{}^{o}C$

Correct answer

A. $434{\text{J kg}}^{- 1}{}^{o}C$

Step-by-step solution

Let $S$ be the specific heat of aluminium

$Q$ given = $Q$ used

$⇒ 1000 \times 0.2 \times S \times ( 150 - 40 ) = 150 \times 1 \times ( 40 - 27 ) + 25 \times 1 \times ( 40 - 27 )$

$⇒ 200 \times S \times 110 = 150 \times 13 + 25 \times 13$

$⇒ S = \dfrac{13 \times 175}{200 \times 110} = 0.1034cal{g}^{- 1} ° C$

$⇒ S = 103.4 \times 4.2J{kg}^{- 1} ° C$ $= 434J{kg}^{- 1} ° C$

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