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

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $\frac{y t_{2}}{x t_{1}}$
The heat $Δ Q$ given or taken to a substance ( mass m)of specific heat $c$ ,to change its temperature by $t^{o} C$ is given by $Δ Q = m c t$ .
Therefore , the heat $Δ Q$ given to a substance ( mass $x$ g) of specific heat $c$ ,to raise its temperature by $t_{1}^{o} C$ is given by $Δ Q = x c t_{1}$ and the heat $Δ Q^{'}$ taken from water ( mass $y$ g) of specific heat $c^{'}$ ,to raise its temperature by $t_{2}^{o} C$ is given by $Δ Q^{'} = y c^{'} t_{2}$
but as $Δ Q = Δ Q^{'}$ ,
Hence, $x c t_{1} = y c^{'} t_{2}$ (for water, specific heat $c^{'} = 1 c a l / g^{o} C$ ) ,
Therefore $c = \frac{y t_{2}}{x t_{1}}$

Suggest Corrections

Similar questions

t_{1} C

t_{2} C

t_{1}^{o} C

t_{2}^{o} C

^{o}

1.

1 k g

1

2.

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

c a l g^{- 1}^{\circ} C^{- 1}

3.

1

Join BYJU'S Learning Program