An aluminium sphere is dipped into the water. Which of the following is true?

As the temperature is increased, the period of a pendulum:

Heat is associated with:

The radius of a metal sphere at room temperature T is R and the coefficient of linear expansion of the metal is $\alpha$. The sphere heated a little by a temperature $∆$T so that its new temperature is T+$∆$T. The increase in the volume of the sphere is approximately:

A sphere, a cube and a thin circular plate, all of the same material and same mass are initially heated to the same high temperature.

Gulab Jamuns (assumed to be spherical) are to be heated in an oven. They are available in two sizes, one twice bigger (in radius) than the other. Pizzas (assumed to be discs) are also to be heated in the oven. They are also in two sizes, one twice bigger (in radius) than the other. All four are put together to be heated to oven temperature. Choose the correct options from the following.

(a) Both size gulab jamuns will get heated in the same time

(b) Smaller gulab jamuns are heated before bigger ones

(c) Smaller pizzas are heated before bigger ones

(d) Bigger pizzas are heated before smaller

Refer to the plot of temperature versus time (figure) showing the changes in the state of ice on heating (not to scale). Which of the following is correct?

(a) The region AB represents the ice and water in thermal equilibrium.

(b) At B, the water starts boiling.

(c) At C, all the water gets converted into steam.

(d) C to D represents water and steam in equilibrium at boiling point.

A glass full of hot milk is poured on the table. It begins to cool gradually. Which of the following is correct?

(a) The rate of cooling is constant till milk attains the temperature of the surrounding.

(b) The temperature of milk falls off exponentially with time.

(c) While cooling, there is a flow of heat from milk to the surrounding as well as from surrounding to the milk but the net flow of heat is from milk to the surrounding and that is why it cools.

(d) All three phenomenon, conduction, convection and radiation are responsible for the loss of heat from milk to the surroundings.

Three stars A, B, and C have surface temperatures ${\mathrm{T}}_{\mathrm{A}}, {\mathrm{T}}_{\mathrm{B}}, \mathrm{and} {\mathrm{T}}_{\mathrm{C}}$ respectively. Star A appears bluish, star B appears reddish and star C yellowish. Hence,

The coefficient of area expansion $\left(\beta \right)$ of a rectangular sheet of a solid in terms of the coefficient of linear expansion $\alpha$ is:

A blacksmith fixes an iron ring on the rim of the wooden wheel of a horse cart. The diameter of the rim and the iron ring are 5.012 m and 5.00 m, respectively at 27 °C. To what temperature should the ring be heated so as to fit the rim of the wheel?

(Given: $\mathrm{\alpha } \mathrm{for} \mathrm{iron}=1.20\times {10}^{-5} °{\mathrm{C}}^{-1}$)

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:

A sphere of 0.047 kg aluminium is placed for sufficient time in a vessel containing boiling water so that the sphere is at 100 °C. It is then immediately transferred to a 0.14 kg copper calorimeter containing 0.25 kg water at 20 °C. The temperature of water rises and attains a steady-state at 23 °C. The specific heat capacity of aluminium is:

(Given that: Specific heat capacity of copper calorimeter = $0.386\times {10}^3 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$ and 

the specific heat capacity of water $\left({\mathrm{s}}_{\mathrm{w}}\right) = 4.18\times {10}^3 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$)

When 0.15 kg of ice at 0 °C is mixed with 0.30 kg of water at 50 °C in a container, the resulting temperature is 6.7 °C. The heat of fusion of ice is: $\left({\mathrm{s}}_{\mathrm{water}} = 4186 \mathrm{J} {\mathrm{kg}}^{-1} \mathrm{K}\right)$

The heat required to convert 3 kg of ice at –12 °C kept in a calorimeter to steam at 100 °C at atmospheric pressure is:

(Given, the specific heat capacity of ice = $2100 \mathrm{J} {\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$, the specific heat capacity of water = $4186 {\mathrm{Jkg}}^{-1}{\mathrm{K}}^{-1}$, the latent heat of fusion of ice = $3.35\times {10}^5 \mathrm{J} {\mathrm{kg}}^{-1}$
and the latent heat of steam = $2.256\times {10}^6 \mathrm{J} {\mathrm{kg}}^{-1}$.)

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 = $385 \mathrm{J} {\mathrm{s}}^{-1} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}$).

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:

A pan filled with hot food cools in 2 minutes from 94 °C to 86 °C when the room temperature is 20 °C. How long will it take to cool from 71 °C to 69 °C?

An iron bar $\left({\mathrm{L}}_1 = 0.1 \mathrm{m}, {\mathrm{A}}_1 0.02 {\mathrm{m}}^2, {\mathrm{K}}_1 = 79 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}\right)$ 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:

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

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

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

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:

A cup of coffee cools from $90° \mathrm{to} 80°$C in t minutes, when the room temperature is $20°\mathrm{C}$. The time taken by a similar cup of coffee to cool from $80° \mathrm{to} 60°$C at room temperature same at $20°\mathrm{C}$ is :