Thermometry, Thermal Expansion and Calorimetry

The length of mercury column in a mercury-in-glass thermometer is $H_1$ mm at the ice point and $H_2$ mm at the steam point. When the length is $H$ mm, the temperature $T$ is given in $^\circ$C by ($H_1 < H_2$)

If the two temperatures on Fahrenheit scale differ by $54^\circ$F, then the difference in temperature on the Celsius scale is

What is the change in volume of an iron sphere of volume $400$ cm$^3$, when it is heated from $0^\circ\text{C}$ to $50^\circ\text{C}$? ($\alpha_{\text{iron}} = 12 \times 10^{-6}/^\circ\text{C}$)

The temperature of a metallic sphere of radius $R$ is increased by a small amount $\Delta T$. If the linear coefficient of thermal expansion of the metal is $\alpha$, the approximate increase in the volume of the sphere is:

The coefficient of volume expansion of mercury is $18 \times 10^{-5}/^\circ$C. A thermometer bulb has volume $10^{-6}$ m$^3$ and cross-section of stem is $0.004$ cm$^2$. Assuming bulb is filled with mercury at $0^\circ$C then the mercury column at $100^\circ$C is

A celsius and a Fahrenheit thermometer are dipped in boiling water. The temperature of water is lowered until the Farenheit thermometer shows $140^\circ$. What is the fall in temperature on the Celsius thermometer?

An iron tyre is to be fitted on to a wooden wheel $1.0$ m in diameter. The diameter of the tyre is $6$ mm smaller than that of the wheel. The tyre should be heated so that its temperature increases by a minimum of

(coefficient of volume expansion of iron = $3.6 \times 10^{-5}/^\circ$C)

The temperature of a metal strip having coefficient of linear expansion $\alpha$ is increased from $T_1$ to $T_2$ resulting in increase of its length by $\Delta L_1$. The temperature is further increased from $T_2$ to $T_3$ such that the increase in its length is $\Delta L_2$.

Given $T_3 + T_1 = 2T_2$ and $T_2 - T_1 = \Delta T$, the value of $\Delta L_2$ is ______.

An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at $30^\circ\text{C}$. The coefficient of linear expansion of aluminium and steel are $24 \times 10^{-6}/^\circ\text{C}$ and $1.2 \times 10^{-5}/^\circ\text{C}$, respectively. The length of this composite rod when its temperature is raised to $100^\circ\text{C}$, is ______ cm.

A sheet of solid material having area $A$ and coefficient of linear expansion $\alpha$. The mass of sheet is $m$ and specific heat capacity is $s$. If $dQ$ is the amount of heat given to the sheet then change in its area is

An ideal gas at pressure $P$ and temperature $T$ is expanding such that $PT^3 =$ constant. The coefficient of volume expansion of the gas is ______.

A metal rod (A) of length $20$ cm expands by $0.075$ cm when its temperature changes from $0^{\circ}$C to $100^{\circ}$ C. Another metal rod (B) of different metal of same length expands by $0.045$ cm for same temperature change. A third rod of same length is composed of 2 parts, one of metal A and another of metal B. For same temperature change, this rod expands by $0.060$ cm. The portion made of metal A has the length

The temperature of a body on Kelvin scale is ' $x$ ' $K$. When it is measured by a Fahrenheit thermometer, it is found to be ' x ' $^\circ\text{F}$. The value of ' $x$ ' is (nearly)

A centigrade and Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenheit temperature observed is $140^\circ\text{F}$. At that time the temperature registered by the centigrade thermometer is

Which of the following figure represents the relation between Celsius and Fahrenheit temperatures?

The volume of a metal sphere increases by $0.33\%$ when its temperature is raised by $50^\circ\text{C}$. The coefficient of linear expansion of the metal is

A thermometer bulb has volume $10^{-6}\text{ m}^3$ and cross-section of the stem is $0.002\text{ cm}^2$. The bulb is filled with mercury at $0^\circ\text{C}$. If the thermometer reads temperature as $100^\circ\text{C}$, then the length of mercury column is (coefficient of cubical expansion of mercury $= 18 \times 10^{-5}/^\circ\text{C}$)

The length of steel rod is 5 cm longer than the copper rod at all temperatures. The length of the steel and copper rod is respectively (Coefficient of linear expansion for steel and copper is respectively $1.1 \times 10^{-5}/^\circ\text{C}$ and $1.7 \times 10^{-5}/^\circ\text{C}$)

The difference in length between two rods A and B is 60 cm at all temperatures. If $\alpha_{\text{A}} = 18 \times 10^{-6}/^\circ\text{C}$ and $\alpha_{\text{B}} = 27 \times 10^{-6}/^\circ\text{C}$, then the length of $\text{rod A}$ and $\text{rod B}$ at $0^\circ\text{C}$ is respectively

Two rods of different materials have lengths ' $l_1$ ' and ' $l_2$ ' whose coefficient of linear expansions are ' $\alpha_1$ ' and ' $\alpha_2$ ' respectively. If the difference between the two lengths is independent of temperature then

Consider a rectangular sheet of solid material of length $l = 9\text{ cm}$ and width $\text{d} = 4\text{ cm}$. The coefficient of linear expansion is $\alpha = 3.1 \times 10^{-5}\text{ K}^{-1}$ at room temperature and one atmospheric pressure. The mass of sheet $m = 0.1\text{ kg}$ and the specific heat capacity $C_{\text{v}} = 900\text{ J kg}^{-1}\text{ K}^{-1}$. If the amount of heat supplied to the material is $8.1 \times 10^2\text{ J}$ then change in area of the rectangular sheet is:

On Celsius scale the temperature of body increases by $40^\circ\text{C}$. The increase in temperature on Fahrenheit scale is:

A metal rod having coefficient of linear expansion $2 \times 10^{-5}/^\circ\text{C}$ is 0.75 m long at $45^\circ\text{C}$. When the temperature rises to $65^\circ\text{C}$, the increase in length of the rod will be

The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $8\ \Omega$ and $10\ \Omega$ respectively. After inserting in a hot bath of temperature $400^\circ\text{C}$, the resistance of platinum wire is:

At certain temperature, $\text{rod A}$ and $\text{rod B}$ of different materials have lengths $\text{L}_{\text{A}}$ and $\text{L}_B$ respectively. Their co-efficients of linear expansion are $\alpha_A$ and $\alpha_B$ respectively. It is observed that the difference between their lengths remain constant at all temperatures. The ratio $L_A/L_B$ is given by

Rails of material of steel are laid with gaps to allow for thermal expansion. Each track is 10 m long, when laid at temperature $17^\circ\text{C}$. The maximum temperature that can be reached is $45^\circ\text{C}$. The gap to be kept between the two segments of railway track is

$(\alpha$steel $= 1.3 \times 10^{-5}/^\circ\text{C})$

At certain temperature, $\text{rod A}$ and $\text{rod B}$ of different materials have lengths $\text{L}_{\text{A}}$ and $\text{L}_{\text{B}}$ respectively. Their coefficients of linear expansion are $\alpha_A$ and $\alpha_B$ respectively. It is observed that the difference between their lengths remains constant at all temperatures. The ratio $\text{L}_{\text{A}} : \text{L}_{\text{B}}$ is given by

Railway track is made of steel segments separated by small gaps to allow for linear expansion. The segment of track is 10 m long when laid at temperature $17^\circ\text{C}$. The maximum temperature that can be reached is $45^\circ\text{C}$. Increase in length of the segment of railway track is ' $x$ ' $\times 10^{-5}\text{ m}$. The value of ' $x$ ' is $(\alpha$steel $= 1.2 \times 10^{-5}/^\circ\text{C})$

A sheet of steel is 40 cm long and 5 cm broad at $0^\circ\text{C}$. The surface area of the sheet increases by $1.4\text{ cm}^2$ at $100^\circ\text{C}$. Coefficient of linear expansion of steel is

Two rods, one of copper ( Cu$)$ and the other of iron ( Fe) having initial lengths $L_1$ and $L_2$ respectively are connected together to form a single rod of length $L_1 + L_2$. The coefficient of linear expansion of Cu and Fe are $\alpha_c$ and $\alpha_i$ respectively. If the length of each rod increases by the same amount when their temperatures are raised by $t^{\circ}\text{C}$, then ratio of $\frac{L_1 - L_2}{L_1 + L_2}$ will be

Two rods, one of aluminium and the other of steel, having initial lengths ' $L_1$ ' and ' $L_2$ ' are connected together to form a single rod of length $(L_1 + L_2)$. The coefficients of linear expansion of aluminium and steel are ' $\alpha_1$ ' and ' $\alpha_2$ ' respectively. If the length of each rod increases by the same amount, when their temperatures are raised by $t^{\circ}\text{C}$, then the ratio $\frac{L_1}{L_1 + L_2}$ will be

A metal rod $2\text{ m}$ long increases in length by $1.6\text{ mm}$, when heated from $0^\circ\text{C}$ to $60^\circ\text{C}$. The coefficient of linear expansion of metal rod is

The volume of a metal block increases by $0.225\%$ when its temperature is increased by $30^\circ\text{C}$. Hence coefficient of linear expansion of the material of metal block is

On a temperature scale '$\text{X}$', the boiling point of water is $65^\circ\text{X}$ and the freezing point is $-15^\circ\text{X}$. Assume that the $\text{X}$ scale is linear. The equivalent temperature corresponding to $-95^\circ\text{X}$ on the Fahrenheit scale would be:

The graph between two temperature scales P and Q is shown in the figure. Between upper fixed point and lower fixed point there are 150 equal divisions of scale P and 100 divisions on scale Q. The relationship for conversion between the two scales is given by :-

A faulty thermometer reads $5^\circ\text{C}$ in melting ice and $95^\circ\text{C}$ in steam. The correct temperature on absolute scale will be __________ $\text{K}$ when the faulty thermometer reads $41^\circ\text{C}$.

The difference in length between two rods $\text{A}$ and $\text{B}$ is $60\text{ cm}$ at all temperatures. If $\alpha_{\text{A}} = 18 \times 10^{-6}/^\circ\text{C}$ and $\alpha_{\text{B}} = 27 \times 10^{-6}/^\circ\text{C}$, the lengths of the two rods are

The side of a copper cube is $1\text{ m}$ at $0^\circ\text{C}$. What will be the change in its volume, when it is heated to $100^\circ\text{C}$? $[\alpha$copper $= 18 \times 10^{-6}/^\circ\text{C}]$

Two uniform brass rods $A$ and $B$ of length '$l$' and '$2l$' and their radii '$2r$' and '$r$' respectively are heated to same temperature. The ratio of the increase in the volume of $\text{rod A}$ to that of $\text{rod B}$ is

A hole is drilled in a metal sheet. At $27^\circ\text{C}$, the diameter of hole is 5 cm. When the sheet is heated to $177^\circ\text{C}$, the change in the diameter of hole is $\text{d} \times 10^{-3}$ cm. The value of d will be __________ if coefficient of linear expansion of the metal is $1.6 \times 10^{-5}/^\circ$C.

A steel rod of length $1\text{ m}$ and cross sectional area $10^{-4}\text{ m}^2$ is heated from $0^\circ\text{C}$ to $200^\circ\text{C}$ without being allowed to extend or bend. The compressive tension produced in the rod is ___________ $\times 10^4\text{ N}$. (Given Young's modulus of steel $= 2 \times 10^{11}\text{ N m}^{-2}$, coefficient of linear expansion $= 10^{-5}\text{ K}^{-1}$)