Physics Thermal Properties of Matter

A non-isotropic solid metal cube has coefficients of linear expansion as: $5*{10}^{-5}/{}^{\circ }\mathrm{C}$  along the $x=$  axis and $5*{10}^{-6}/{}^{\circ }\mathrm{C}$  along the $y$  and the $z$ -axis. If coefficient of volume expansion of the solid $\mathrm{C}*{10}^{-6}/{}^{\circ }\mathrm{C}$  then the value of $\mathrm{C}$  is                   

$\mathrm{M}$ grams of steam at  ${100}^{\circ }\mathrm{C}$ is mixed with $200\mathrm{g}$ of ice at its melting point in a thermally insulated container. If it produces liquid water at ${40}^{?}\mathrm{C}$ [heat of vaporization of water is $540\mathrm{c}\mathrm{a}\mathrm{l}/\mathrm{g}$ and heat of fusion of ice is $80\mathrm{c}\mathrm{a}\mathrm{l}/\mathrm{g}$ ], the value of $M$  is     

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

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

Two metallic blocks M₁ and M₂ of same area of cross – section are connected to each other (as shown in figure). If the thermal conductivity of M₂ is K then thermal conductivity of M₁ will be :

[Assume steady state heat conduction]

As per the given figure, two plates A and B of thermal conductivity K and 2K are joined together of form a compound plate. The thickness of plates are 4.0cm and 2.5cm respectively and the area the area of cross-section is 120 cm² for each plate. The equivalent thermal is 120 cm² for each plate. The equivalent thermal conductivity of the compound plat is $\left(1+\frac{5}{\alpha }\right)K,$  then the value of a will be________.

An ice cube of dimensions 60cm * 50cm * 20cm is placed in an insulation box of wall thickness 1cm. The box keeping the ice cube at $0°C$ 898

of temperature is brought to a room of temperature $40°C.$ The rate of melting of ice is approximately:

(Latent heat of fusion of ice is 3.4 * 105 J kg1 and thermal conducting of insulation wall is 0.05 $W{m}^{-1}°C^{-1}$ )