If there are no heat losses, the heat released by the condensation of $x$ gm of steam at $100^o C$ into water at $100^o C$ can be used to convert $y$ gm of ice at $0^o C$ into water at $100^o C$. Then the ratio $y : x$ is nearly

A pendulum clock keeps correct time at $0\ ^oC$. The thermal coefficient of linear expansion of the  material of the pendulum is $\alpha$. If the temperature rises to $t\ ^oC$, then the clock loses per day by (in second)

A block of ice at $-10\,^oC$ is slowly heated and converted to steam at $100\,^oC.$ Which of the following curves represent the phenomenon qualitatively ?

A cylindrical rod with one end in a steam chamber and the outer end in ice results in melting of $0.1 \,\,gm$ of ice per second. If the rod is replaced by another with half the length and double the radius of the first and if the thermal conductivity of material of second rod is $1/4$ that of first, the rate at which ice melts is $gm/sec$ will be

A steel ball of mass $0.1 kg$ falls freely from a height of $10 m$ and bounces to a height of $5.4m$ from the ground. If the dissipated energy in this process is absorbed by the ball, the rise in its temperature is ……….. $^\circ \mathrm{C}$ (Specific heat of steel $ = 460\,Joule – k{g^{ – 1}}^\circ {C^{ – 1}},\;g = 10\,m{s^{ – 2}}$)