A unit scale is to be prepared whose length does not change with temperature and remains $20 \mathrm{cm}$, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is $40 \mathrm{cm}$ and length of iron will be _____ $\mathrm{cm}$.

$\left({\alpha }_{\mathrm{iron} }=1.2\times {10}^{-5}{ \mathrm{K}}^{-1}\right.$ and $\left.{\alpha }_{\mathrm{brass} }=1.8\times {10}^{-5}{ \mathrm{K}}^{-1}\right)$.

A block of ice of mass $120 \mathrm{g}$ at temperature $0°\mathrm{C}$ is put in $300 \mathrm{g}$ of water at $25°\mathrm{C}$. The $x \mathrm{g}$ of ice melts as the temperature of the water reaches $0°\mathrm{C}$. The value of $x$ is

[Use: Specific heat capacity of water $=4200 \mathrm{J} {\mathrm{kg}}^{-1}{ \mathrm{K}}^{-1}$, Latent heat of ice $=3.5\times {10}^5 \mathrm{J} {\mathrm{kg}}^{-1}$]

If $K_1$ and $K_2$ are the thermal conductivities $L_1$ and $L_2$ are the lengths and $A_1$ and $A_2$ are the cross sectional areas of steel and copper rods respectively such that $\frac{K_2}{K_1}=9,\frac{A_1}{A_2}=2,\frac{L_1}{L_2}=2$. Then, for the arrangement as shown in the figure. The value of temperature $T$ of the steel - copper junction in the steady state will be

The graph between two temperature scales $P$ and $Q$ is shown in the figure. Between upper fixed point and lower fixed point there are $150$ equal divisions of scale $P$ and $100$ divisions on scale $Q$. The relationship for conversion between the two scales is given by :

.