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Calorimetry

A certain amo...

Question

A certain amount of heat is required to raise the temperature of x gram of a substance through $t_{1} C$ . The same amount of heat when taken away from y gram of water, it cools through $t_{2} C$ . Therefore, the specific heat of the substance is

\frac{y t_{1}}{x t_{1}}

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\frac{x t_{2}}{y t_{1}}

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\frac{y t_{2}}{x t_{1}}

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\frac{x t_{1}}{y t_{1}}

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Solution

The correct option is C $\frac{y t_{2}}{x t_{1}}$
For that substance,
$Δ Q = m s_{1} Δ T$ = $(x) (s_{1}) (t_{1})$ ..........(1)
Where $s_{1}$ is specific heat of substance

For water,
$Δ Q = m^{'} s_{2} Δ T$ = $(y) (s_{2}) (t_{2})$ ..........(2)
Where $s_{2}$ is specific heat of water

From eq (1) and (2) we get,

$(x) (s_{1}) (t_{1})$ = $(y) (s_{2}) (t_{2})$

$\frac{s_{1}}{s_{2}} = \frac{y t_{2}}{x t_{1}}$

Hence, option C is the correct answer and options A is incorrect.

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