Physics Thermal Properties of Matter

Two identical metal of thermal conductivities K₁ and K₂ respectively are connected in series. The effective thermal conductivity of the combination is:

Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity K₁, K₂, and K₃, respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at 100°C and the other at 0°C (see figure). If the joints of the rod are at 70°C and 20°C in steady state and there is no loss of energy from the surface of the rod, the correct relationship between K₁, K₂ and K₃ is:

A bakelite beaker has volume capacity of 500cc at 30°C. When it is partially filled with V? volume (at 30°C) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If γ(beaker) = 6 × 10? °C?¹ and γ(mercury) = 1.5 × 10? °C?¹, where γ is the coefficient of volume expansion, then V? (in cc) is close to
(Heat)

Two different wires having lengths $L_1$ ${}_{}$ and ${}_{}$ $L_2$ , and respective temperature coefficient of linear 4expansion ${\alpha }_1$ ${}_{}$ and ${\alpha }_2$ ${}_{}$ , are joined end-to-end. Then the effective temperature coefficient of linear expansion 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 ${40}^{\circ }\mathrm{C}$ [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 bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal A has higher coefficient of expansion compared to that metal B. When bimetallic strip is placed in a cold bath, it will

Two different metal bodies A and B of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. The ratio of specific heat capacities is :
(The graph shows Temperature (°C) on the y-axis and Time (s) on the x-axis. Both A and B are straight lines starting from the origin. For body A, temperature reaches 120°C in 4s. For body B, temperature reaches 90°C in 6s.)

Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is 'a'. The metal sheet is heated uniformly, bya small temperature   $\Delta T,$ so that its new temperature is T +   $\Delta T.$ Calculate the increase in the volume of the metal box.