Two rods, one made of copper and other made of steel, of the same length and same cross sectional area are joined together. The thermal conductivity of copper and steel are \(385~\text{Js}^{-1}\text{K}^{-1}\text{m}^{-1}\) and \(50~\text{Js}^{-1}\text{K}^{-1}\text{m}^{-1}\) respectively. The free ends of copper and steel are held at \(100^\circ \text{C}\) and \(0^\circ \text{C}\) respectively. The temperature at the junction is, nearly:
1. \(12^\circ \text{C}\)
2. \(50^\circ \text{C}\)
3. \(73^\circ \text{C}\)
4. \(88.5^\circ \text{C}\)

A cup of coffee cools from \(90^{\circ}\mathrm{C}\) $\mathrm{to}$ \(80~^{\circ}\mathrm{C}\) in t minutes, when the room temperature is \(20^{\circ}\mathrm{C}\)$\mathrm{}$. The time taken by a similar cup of coffee to cool from \(80^{\circ}\mathrm{C}\) $\mathrm{to}$ \(60^{\circ}\mathrm{C}\) at room temperature same at \(20^{\circ}\mathrm{C}\) is:
1. \(\frac{10}{13}t\) 
2. \(\frac{5}{13}t\)
3. \(\frac{13}{10}t\)
4. \(\frac{13}{5}t\)

The diagram below shows a graphical representation of pressure versus temperature variation for three different low-density gases A, B & C.

Which of the following can be deduced about absolute zero for the gases A, B & C:

1. Different for all the three gases

2. Same only for gases A & B 

3. Same only for gases B & C

4. Same for all the three gases

The figure shows pressure versus temperature graph for a low-density gas kept in a vessel with:

1. Variable volume

2. Volume first increasing then decreasing

3. Volume first decreasing then increasing

4. Constant volume

The given graph shows the variation of Fahrenheit temperature ($t_F$) vs Celsius temperature ($t_C$). The correct relation between the two temperature scales that can be deduced from the graph below is

$1. \frac{t_F}{t_C}=\frac{5}{9}$
$2. \frac{t_F-32}{t_C}=\frac{212-32}{100-0}$
$3. \frac{t_F-32}{t_C}=\frac{100-0}{212-32}$
$4. \frac{t_F}{t_C}=\frac{212-32}{100-0}$

An iron bar $\left({\mathrm{L}}_1 = 0.1 \mathrm{m}, {\mathrm{A}}_1 0.02 {\mathrm{m}}^2, {\mathrm{K}}_1 = 79 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}\right)$ and a brass bar $\left({\mathrm{L}}_2 = 0.1 \mathrm{m}, {\mathrm{A}}_2 = 0.02 {\mathrm{m}}^2, {\mathrm{K}}_2 = 109 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}\right)$ are soldered end to end as shown in the figure. The free ends of the iron bar and brass bar are maintained at 373 K and 273 K respectively. The heat current through the compound bar is:

1.  $916.1 \mathrm{W}$

2.  $826.1 \mathrm{W}$

3.  $926.1 \mathrm{W}$

4.  $726 \mathrm{W}$

An iron bar $\left({\mathrm{K}}_1 = 79 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}\right)$ and a brass bar $\left({\mathrm{K}}_2 = 109 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}\right)$ are soldered end to end as shown in the figure. The free ends of the iron bar and brass bar are maintained at 373 K and 273 K respectively and the  The equivalent thermal conductivity of the compound bar is:

1.  $94.6 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}$

2.  $93.6 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}$

3.  $81.6 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}$

4.  $91.6 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}$

A pan filled with hot food cools in 2 minutes from \(94^{\circ}\mathrm{C}\) to \(86^{\circ}\mathrm{C}\) when the room temperature is \(20^{\circ}\mathrm{C}\). How long will it take to cool from \(71^{\circ}\mathrm{C}\) to \(69^{\circ}\mathrm{C}\)?

An iron bar $\left({\mathrm{L}}_1 = 0.1 \mathrm{m}, {\mathrm{A}}_1=0.02 {\mathrm{m}}^2, {\mathrm{K}}_1=79 {\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}\right)$ and a brass bar$\left({\mathrm{L}}_2 = 0.1 \mathrm{m}, {\mathrm{A}}_2 = 0.02 {\mathrm{m}}^2, {\mathrm{K}}_2 = 109 {\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}\right)$ are soldered end to end as shown in the figure. The free ends of the iron bar and brass bar are maintained at 373 K and 273 K respectively. The temperature of the junction of the two bars is:

1.  $215 \mathrm{K}$

2.  $315 \mathrm{K}$

3.  $415 \mathrm{K}$

4.  $115 \mathrm{K}$

What is the temperature of the steel-copper junction in the steady-state of the system shown in the figure?

The length of the steel rod = 15.0 cm, length of the copper rod = 10.0 cm, temperature of the furnace = 300 °C, temperature of the other end = 0 °C. The area of the cross section of the steel rod is twice that of the copper rod.

(Thermal conductivity of steel = $50.2 \mathrm{J} {\mathrm{s}}^{-1} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}$; and of copper = $385 \mathrm{J} {\mathrm{s}}^{-1} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}$).

1.  $44.4 °\mathrm{C}$

2.  $44.4 \mathrm{K}$

3.  $54.4 °\mathrm{C}$

4.  $54.4 \mathrm{K}$