A metallic bar of Young's modulus \(0.5 \times 10^{11}~\text{Nm}^{-2},\)  coefficient of linear thermal expansion \(10^{-5} ~^{\circ}\text{C}^{-1},\) length \(1~\text m\) and cross-sectional area \(10^{-3} ~\text{m}^2\) is heated from \(0^\circ \text{C}\) to \(100^\circ \text C\) without expansion or bending. The compressive force developed in the metallic bar is: 
1. \(50 \times 10^3~ \text N\)
2. \(100 \times 10^3 ~\text N\)
3. \(2 \times 10^3~\text N\)
4. \(5 \times 10^3 ~\text N\)

A cup of coffee cools from \(90^{\circ}\text{C}\) $\mathrm{to}$ \(80^{\circ}\text{C}\) in \(t\) minutes, when the room temperature is \(20^{\circ}\text{C}.\)$\mathrm{}$ The time taken by a similar cup of coffee to cool from \(80^{\circ}\text{C}\) $\mathrm{to}$ \(60^{\circ}\text{C}\) at room temperature same at \(20^{\circ}\text{C}\) 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 \(\left(L_{1} = 0 . 1 ~ \text{m},   A_{1} =  0 . 02 ~\text{m}^{2}, K_{1} = 79~\text{W m}^{- 1} \text{K}^{- 1}\right)\) and a brass bar \(\left(L_{2}= 0 . 1 ~\text{m}, A_2 = 0.02~\text{m}^2, K_2 = 109~\text{W m}^{-1}\text{K}^{-1}\right)\) 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. \(916.1\) W
2. \(826.1\) W
3. \(926.1\) W
4. \(726\) W

An iron bar \(K_1 = 79~\text{W m}^{-1}\text{K}^{-1}\) and a brass bar \(K_2 = 109~\text{W m}^{-1}\text{K}^{-1}\) 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. Then the equivalent thermal conductivity of the compound bar is:

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

1. \(215~ \text{K}\) 
2. \(315~ \text{K}\) 
3. \(415~ \text{K}\) 
4. \(115~ \text{K}\)