Three rods of equal length $l$  are joined to form an equilateral triangle $PQR.$  $O$  is the mid point of $PQ.$  Distance $OR$  remains same for small change in temperature. Coefficient of linear expansion for $PR$ and $RQ$  is same, $i.e., \alpha _2$  but that for $PQ$  is $\alpha _1.$ Then

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 ?

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

Steam at $100\,^oC$ is passed into $22\,g$ of water at $20\,^oC$  The mass of water that will be present when the water acquires a temperature of $90\,^oC$  (Latent heat of steam is $540\,cal/g$) is ......... $\mathrm{g}$

On a new scale of temperature (which is linear) and called the $W$ scale, the freezing and boiling points of water are $39\,^oW$ and $239\,^oW$ respectively. What will be the temperature on the new scale, corresponding to a temperature of $39\,^oC$ on the Celsius scale ? ............. $^\circ \mathrm{W}$

Steam at $100\,^oC$ is passed into $1.1\,kg$ of water contained in calorimeter of water equivalent $0.02\ kg$ at $15\,^oC$ till the temperature of the calorimeter rises to $80\,^oC$. The mass of steam condensed in kilogram is