…………  $gm$ of a liquid of specific heat $0.2$ at a temperature $40°C$ must be mixed with $100 \,gm$ of a liquid of specific heat of $0.5 $ at a temperature $20°C,$ so that the final temperature of the mixture becomes $32°C$

A copper ring has a diameter of exactly $25 \,\,mm$ at its temperature of $0^o C$. An aluminium sphere has a diameter of exactly $25.05\,\, mm$ at its temperature of $100^o C$. The sphere is placed on top of the ring and two are allowed to come to thermal equilibrium, no heat being lost to the surrounding. The sphere just passes through the ring at the equilibrium temperature. The ratio of the mass of the sphere & ring is : (given : $\alpha_{Cu} = 17 × 10^{-6} /^o C, \alpha = 2.3 × 10^{-5} /^o C,$ specific heat of $Cu = 0.0923 Cal/g^o C$ and specific heat of $Al = 0.215 cal/g^o C$)

A system $S$ receives heat continuously from an electrical heater of power $10W$. The temperature of S becomes constant at $50^o C$ when the surrounding temperature is $20^o C$. After the heater is switched off, $S$ cools from $35.1^o C$ to $34.9^o C$ in $1$ minute. The heat capacity of $S$ is…….. $ J/^oC$

A bullet of mass $5\, g$, travelling with a speed of $210$ $m / s ,$ strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the bullet while the other half is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is $0.030\, cal /\left( g -{ }^{\circ} C \right)$ $\left(1\, cal =4.2 \times 10^{7}\, ergs \right)$ close to$…….^oC$

The density of a material $A$ is $1500 kg/m^3$ and that of another material $B$ is $2000 kg/m^3$. It is found that the heat capacity of $8$ volumes of $A$ is equal to heat capacity of $12$ volumes of $B$. The ratio of specific heats of $A$ and $B$ will be