A metal bar of length \(L\) and area of cross-section \(A\) is clamped between two rigid supports. For the material of the rod, its Young’s modulus is \(Y\) and the coefficient of linear expansion is \(\alpha\). If the temperature of the rod is increased by \(\Delta t^{\circ} \mathrm{C}\), the force exerted by the rod on the supports will be:
1. \(YAL\Delta t\)
2. \(YA\alpha\Delta t\)
3. \(\frac{YL\alpha\Delta t}{A}\)
4. \(Y\alpha AL\Delta t\)

The pressure applied from all directions on a cube is P. How much its temperature should be raised to maintain the original volume ? The volume elasticity of the cube is  $\beta$ and the coefficient of volume expansion is $\alpha$ -

(1) $\frac{P}{\alpha \beta }$                                 

(2) $\frac{P\alpha }{\beta }$

(3) $\frac{P\beta }{\alpha }$                                 

(4) $\frac{\alpha \beta }{P}$

Under steady state, the temperature of a body 

(1) Increases with time

(2) Decreases with time

(3) Does not change with time and is same at all the points of the body

(4) Does not change with time but is different at different points of the body

The coefficient of thermal conductivity depends upon

(1) Temperature difference of two surfaces

(2) Area of the plate

(3) Thickness of the plate

(4) Material of the plate

When two ends of a rod wrapped with cotton are maintained at different temperatures and, after some time, every point of the rod attains a constant temperature, then:

The ratio of thermal conductivity of two rods of different material is 5 : 4. The two rods of same area of cross-section and same thermal resistance will have the lengths in the ratio 

(1) 4 : 5             

(2) 9 : 1

(3) 1 : 9             

(4) 5 : 4

In variable state, the rate of flow of heat is controlled by
(1) Density of material               

(2) Specific heat

(3) Thermal conductivity             

(4) All the above factors

The dimensions of thermal resistance are
(1) ${\mathrm{M}}^{-1}{\mathrm{L}}^{-2}{\mathrm{T}}^3\mathrm{K}$           

(2) ${\mathrm{ML}}^2{\mathrm{T}}^{-2}{\mathrm{K}}^{-1}$

(3) ${\mathrm{ML}}^2{\mathrm{T}}^{-3}\mathrm{K}$               

(4) ${\mathrm{ML}}^2{\mathrm{T}}^{-2}{\mathrm{K}}^{-2}$

Two walls of thicknesses ${\mathrm{d}}_1$ and ${\mathrm{d}}_2$ and thermal conductivities ${\mathrm{k}}_1$ and ${\mathrm{k}}_2$ are in contact. In the steady state, if the temperatures at the outer surfaces  are ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$, the temperature at the common wall is  -

(1) $\frac{{\mathrm{k}}_1{\mathrm{T}}_1{\mathrm{d}}_2+{\mathrm{k}}_2{\mathrm{T}}_2{\mathrm{d}}_1}{{\mathrm{k}}_1{\mathrm{d}}_2+{\mathrm{k}}_2{\mathrm{d}}_1}$                     

(2)$\frac{{\mathrm{k}}_1{\mathrm{T}}_1+{\mathrm{k}}_2{\mathrm{d}}_2}{{\mathrm{d}}_1+{\mathrm{d}}_2}$

(3) $\left(\frac{{\mathrm{k}}_1{\mathrm{d}}_1+{\mathrm{k}}_2{\mathrm{d}}_2}{{\mathrm{T}}_1+{\mathrm{T}}_2}\right){\mathrm{T}}_1{\mathrm{T}}_2$                   

(4) $\frac{{\mathrm{k}}_1{\mathrm{d}}_1{\mathrm{T}}_1+{\mathrm{k}}_2{\mathrm{d}}_2{\mathrm{T}}_2}{{\mathrm{k}}_1{\mathrm{d}}_1+{\mathrm{k}}_2{\mathrm{d}}_2}$

A slab consists of two parallel layers of copper and brass of the same thickness and having thermal conductivities in the ratio 1 : 4. If the free face of brass is at 100°C and that of copper at 0°C, the temperature of interface is
1. 80°C               

2. 20°C

3. 60°C               

4. 40°C