Question

Which one of the following would raise the temperature of 20 g of water at 30⁰C most when mixed with? (Specific heat of water is 1 cal/g ⁰ C)

• A. 20 g of water at 40⁰ C
• B. 40 g of water at 35⁰ C
• C. 10 g of water at 80⁰ C
• D. 4 g of water at 80⁰ C

Answer 1

The correct option is D

4 g of water at 80⁰ C

let, $m$ g of water whose temperatrure is ${\theta }_0(>{30}^{\circ })$ and specific heat is $1$ cal/$g^{\circ }$C added to $20$ g of water at ${30}^{\circ }$C heat given by the $m$ g of water
or $m\left(1\right)({\theta }_0-\theta )=20\left(1\right)(\theta -30)$
solving tgis we get, $\theta =\frac{600+m{\theta }_0}{2+m}$
the right hand side is maximum for option $\left(d\right)$.