Liquid oxygen at 50K is heated to 300K at constant pressure of 1 atm. The rate of heating is constant.Which one of the following graphs represents the variation of temperature with time?

A black body at $227°C$ radiates heat at the rate of 7 cal $c{m}^{-2}{s}^{-1}.$ At a temperature of $727°C,$ the rate of heat radiated in the same units will be 

(1) 60                                     

(2) 50

(3) 112                                   

(4) 80

On a new scale of temperature (which is linear) and called the W scale, the freezing and boiling points of water are $39°W$ and $239°W$ respectively. What will be the temperature on the new scale, corresponding to a temperature of $39°C$ on the Celsius scale?

(1) $78°W$                                   

(2) $117°W$

(3) $200°W$                                 

(4) $139°W$

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 coefficient of linear expansion of brass and steel are ${\alpha }_1$ and ${\alpha }_2$. If we take a brass rod of length $l_1$ and steel rod of length $l_2$ at 0°C, their difference in length $\left(l_2-l_1\right)$ will remain the same at a temperature if

(a) ${\alpha }_1{l}_2={\alpha }_2{l}_1$                                   (b) ${\alpha }_1{l}_2^2={\alpha }_2{l}_1^2$

(c) ${\alpha }_1^2{l}_1={\alpha }_2^2{l}_2$                                   (d) ${\alpha }_1{l}_1={\alpha }_2{l}_2$

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

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

Wires A and B have identical lengths and have circular cross-sections. The radius of A is twice the radius of B i.e. ${\mathrm{r}}_{\mathrm{A}}=2{\mathrm{r}}_{\mathrm{B}}$ . For a given temperature difference between the two ends, both wires conduct heat at the same rate. The relation between the thermal conductivities is given by

(1) ${\mathrm{K}}_{\mathrm{A}}=4{\mathrm{K}}_{\mathrm{B}}$                     
(2) ${\mathrm{K}}_{\mathrm{A}}=2{\mathrm{K}}_{\mathrm{B}}$
(3) ${\mathrm{K}}_{\mathrm{A}}={\mathrm{K}}_{\mathrm{B}}/2$                   
(4) ${\mathrm{K}}_{\mathrm{A}}={\mathrm{K}}_{\mathrm{B}}/4$

Two identical plates of different metals are joined to form a single plate whose thickness is double the thickness of each plate. If the coefficients of conductivity of each plate are 2 and 3 respectively, then the conductivity of the composite plate will be:
1. 5
2. 2.4
3. 1.5                 
4. 1.2

The temperature of the hot and cold ends of a 20 cm long rod in a thermal steady state is at \(100^{\circ}\mathrm{C}\) and \(20^{\circ}\mathrm{C}\) respectively. The temperature at the centre of the rod will be:
1. \(50^{\circ}\mathrm{C}\)
2. \(60^{\circ}\mathrm{C}\)
3. \(40^{\circ}\mathrm{C}\)
4. \(30^{\circ}\mathrm{C}\)