Two rods, A and B, of different materials having the same cross-sectional area are welded together as shown in the figure. Their thermal conductivities are $K_1$ and $K_2$. The thermal conductivity of the composite rod will be:

   

1. $\frac{K_1+K_2}{2}$
2. $\frac{3\left(K_1+K_2\right)}{2}$
3. $K_1+K_2$
4. $2\left(K_1+K_2\right)$

A spherical black body with a radius of \(12\) cm radiates \(450\)-watt power at \(500\) K. If the radius were halved and the temperature doubled, the power radiated in watts would be:
1. \(225\)
2. \(450\)
3. \(1000\)
4. \(1800\)

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at ${100}^{°}$ C, while the other one is at $0^{° }$C. If the two bodies are brought into contact, then assuming no heat loss, the final common temperature is -

(1) ${50}^{°} C$

(2) more than ${50}^{°}$C

(3) less than ${50}^{°}$C but greater than $0^{°}$C

(4)  $0 {}_{0}C$

A body cools from a temperature 3T to 2T in10 minutes. The room temperature is T. Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next 10 minutes will be:
1. \(\frac{7}{4}T\)
2. \(\frac{3}{2}T\)
3. \(\frac{4}{3}T\)
4. \(T\)

The coefficients of linear expansion of brass and steel rods are \(\alpha_1\) and \(\alpha_2\), lengths of brass and steel rods are \(l_1\) and \(l_2\) respectively. If (\(l_2-l_1\)) is maintained the same at all temperatures, Which one of the following relations holds good?
1. \(\alpha_1 l_2^2=\alpha_2l_1^2\)
2. \(\alpha_1^2 l_2=\alpha_2^2l_1\)
3. \(\alpha_1 l_1=\alpha_2l_2\)
4. \(\alpha_1 l_2=\alpha_2l_1\)

A black body is at a temperature of 5760 K. The energy of radiation emitted by the body at a wavelength of 250 nm is U₁, at a wavelength of 500 nm is U₂ and that at 1000 nm is U₃. Given Wien's constant $b=2.88\times {10}^6$ $nm-\mathrm{K,\; which }$of the following is correct?
1. U₃=0       
2. U₁>U₂
3. U₂>U₁     
4. U₁=0

Two metal wires of identical dimensions are connected in series. If $\sigma$₁ and $\sigma$₂ are the conductivities of the metal wires respectively, the effective conductivity of the combination is

1. $\frac{{\displaystyle 2{\sigma }_1{\sigma }_2}}{{\displaystyle {\sigma }_1+{\sigma }_2}}$

2. $\frac{{\displaystyle {\sigma }_1{\sigma }_2}}{{\displaystyle 2{\sigma }_1{\sigma }_2}}$ 

3. $\frac{{\displaystyle {\sigma }_1+{\sigma }_2}}{{\displaystyle {\sigma }_1{\sigma }_2}}$  

4. $\frac{{\displaystyle {\sigma }_1{\sigma }_2}}{{\displaystyle {\sigma }_1+{\sigma }_2}}$

The value of coefficient of volume expansion of glycerin is 5x10^-4 K^-1. The fractional change in the density of glycerin for a rise of 40°C in its temperature is -

(1) 0.015

(2) 0.020

(3) 0.025

(4) 0.010

Steam at 100°C is passed into 20 g of water at 10°C. When water acquires a temperature of 80°C, the mass of water present will be (Take specific heat of water=1 cal g^-1 °C^-1 and latent heat of steam = 540 cal g^-1)

(a) 24 g                       

(b) 31.5g

(c) 42.5 g                   

(d) 22.5 g

A certain quantity of water cools from \(70^{\circ}\mathrm{C}\) to \(60^{\circ}\mathrm{C}\) in the first 5 minutes and to \(54^{\circ}\mathrm{C}\) in the next 5 minutes. 
The temperature of the surroundings will be: