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)

$540\  g$ of ice at $0\ ^oC$ is mixed with $540\  g$ water at $80\  ^oC$. The final temperature of the mixture is

Amount of heat required to raise the temperature of a body through $1 ^o C$ is called its

A rod of length $20 \,\,cm$ is made of metal. It expands by $0.075\,\, cm$ when its temperature is raised from $0^o C$ to $100^o C$. Another rod of a different metal $B$ having the same length expands by $0.045 cm$ for the same change in temperature, a third rod of the same length is composed of two parts one of metal $A$ and the other of metal $B$. Thus rod expand by $0.06 \,\,cm$.for the same change in temperature. The portion made of metal $A$ has the length .............. $cm$

If the volume of a block of metal changes by $0.12\%$ when it is heated through $20^o\,C$, the coefficient of linear expansion (in per $^oC^{-1}$) of the metal is :-