A mass of $50\,g$ of water in a closed vessel, with surroundings at a constant temperature takes $2\, minutes$ to cool from $30\,^oC$ to $25\,^oC$. A mass of $100\,g$ of another liquid in an identical vessel with identical surroundings takes the same time to cool from $30\,^oC$ to $25\,^o C$. The specific heat of the liquid is .......... $kcal/kg$ (The water equivalent of the vessel is $30\,g$.)
$2.0$
$7$
$3$
$0.5$
Two liquids $A$ and $B$ are at $32\,^oC$ and $24\,^oC.$ When mixed in equal masses the temperature of the mixture is found to be $28\,^oC$. Their specific heats are in the ratio of
$10 \,gm$ of ice at $-20^{\circ} C$ is kept into a calorimeter containing $10 \,gm$ of water at $10^{\circ} C$. The specific heat of water is twice that of ice. When equilibrium is reached, the calorimeter will contain ..........
A mass of material exists in its solid format its melting temperature $0\,^o C$. The following processes then occur to the material
Process $-1$:An amount of thermal energy $Q$ is added to the material and $\frac{2}{3}$ of the material melts.
Process $-2$:An identical additional amountof thermal energy $Q$ is added to the materlal is now a liquid at $4\,^o C$
........ $^oC$ is the ratio of the latent heat of fusion to the specific heat of the liquid for this material.
A tap supplies water at $10\,^oC$ and another tap at $100\,^oC$. .......... $kg$ hot water must be taken so that we get $20\, kg$ water at $35\,^oC$ ?
A piece of ice (heat capacity $=2100 \mathrm{~J} \mathrm{~kg}^{-1}{ }^{\circ} \mathrm{C}^{-1}$ and latent heat $=3.36 \times 10^5 \mathrm{~J} \mathrm{~kg}^{-1}$ ) of mass $\mathrm{m}$ grams is at $-5^{\circ} \mathrm{C}$ at atmospheric pressure. It is given $420 \mathrm{~J}$ of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that $1 \ \mathrm{gm}$ of ice has melted. Assuming there is no other heat exchange in the process, the value of $m$ is