Thermal Properties of Matter

As shown in the figure, an insulated container is fitted with a thermally conducting but immovable partition $(P_1)$ and a freely movable but thermally insulated piston $(P_2)$. The partition $P_1$ with thermal conductivity $K$, cross sectional area $A$ and width $x$ divides the container into two sections, $S_1$ and $S_2$, each containing one mole of a monoatomic gas. The piston $P_2$ moves freely such that the gas in $S_2$ is always at the atmospheric pressure. Initially, the difference between the temperatures of $S_1$ and $S_2$ is $\Delta T_0$. The time it takes for the temperature difference to become $\dfrac{\Delta T_0}2$ is $nxR/KA$, where $R$ is the universal gas constant. The value of $n$ is:
[Given: $\ln2\approx0.7$]

A nuclear reactor starts producing a radioactive nuclide $X$ from $t=0$, at a constant rate of $\alpha$ per second. Each decay of $X$ produces energy $E_0$, which is utilized to heat a liquid of mass $m$ and specific heat $s$. Assuming no heat loss from the liquid and taking $\lambda$ as the decay constant of $X$, the rate of increase in the temperature of the liquid is:

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

The heat extracted out of $x$ gram of water initially at 50 °C to cool it down to 0 °C is sufficient to evaporate $(1000-x)$ gram of water also initially at 50 °C. The value of $x$ (closest integer ) is ________.

(Take latent heat of water 2256 kJ/kg. K, specific heat capacity of water 4200 J/kg. K)

Two identical plates P and Q, radiating as perfect black bodies, are kept in vacuum at constant absolute temperatures $T_P$ and $T_Q$, respectively, with $T_Q < T_P$, as shown in Fig. 1. The radiated power transferred per unit area from P to Q is $W_0$. Subsequently, two more plates, identical to P and Q, are introduced between P and Q, as shown in Fig. 2. Assume that heat transfer takes place only between adjacent plates. If the power transferred per unit area in the direction from P to Q (Fig. 2) in the steady state is $W_S$, then the ratio $\dfrac{W_0}{W_S}$ is _____.

The specific heat capacity of a substance is temperature dependent and is given by the formula $C = kT$, where $k$ is a constant of suitable dimensions in SI units, and $T$ is the absolute temperature. If the heat required to raise the temperature of $1\,\mathrm{kg}$ of the substance from $-73\,^{\circ}\mathrm{C}$ to $27\,^{\circ}\mathrm{C}$ is $nk$, the value of $n$ is _____.

[Given: $0\,\mathrm{K} = -273\,^{\circ}\mathrm{C}$.]

Match the temperature of a black body given in List-I with an appropriate statement in List-II, and choose the correct option.

[Given: Wien's constant as $2.9\times10^{-3}$ m-K and $\dfrac{hc}{e} = 1.24\times10^{-6}$ V-m]

List I describes thermodynamic processes in four different systems. List II gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process.

Which one of the following options is correct?

Two metallic blocks $M_1$ and $M_2$ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of $M_2$ is $K$ then the thermal conductivity of $M_1$ will be :

[Assume steady state heat conduction]

A 100 g of iron nail is hit by a 1.5 kg hammer striking at a velocity of $60\ \mathrm{ms^{-1}}$. What will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail ?

[Specific heat capacity of iron $=0.42\ \mathrm{Jg^{-1}\,°C^{-1}}$]

In an experiment to verify Newton's law of cooling, a graph is plotted between, the temperature difference ($\Delta T$) of the water and surroundings and time as shown in figure. The initial temperature of water is taken as 80°C. The value of $t_2$ as mentioned in the graph will be ______.

A steam engine intakes 50 g of steam at 100°C per minute and cools it down to 20°C. If latent heat of vaporization of steam is 540 cal g$^{-1}$, then the heat rejected by the steam engine per minute is ______ $\times10^3$ cal.

(Given : specific heat capacity of water : 1 cal g$^{-1}$ °C$^{-1}$)

A solid metallic cube having total surface area 24 m$^2$ is uniformly heated. If its temperature is increased by 10°C, calculate the increase in volume of the cube. (Given $\alpha=5.0\times10^{-4}$ °C$^{-1}$).

A copper block of mass 5.0 kg is heated to a temperature of 500°C and is placed on a large ice block. What is the maximum amount of ice that can melt?

[Specific heat of copper : 0.39 J g$^{-1}$ °C$^{-1}$ and latent heat of fusion of water : 335 J g$^{-1}$]

A geyser heats water flowing at a rate of 2.0 kg per minute from 30°C to 70°C. If geyser operates on a gas burner, the rate of combustion of fuel will be ______ g min$^{-1}$

[Heat of combustion $=8\times10^3$ J g$^{-1}$, Specific heat of water $=4.2$ J g$^{-1}$ °C$^{-1}$]

A lead bullet penetrates into a solid object and melts. Assuming that 40% of its kinetic energy is used to heat it, the initial speed of bullet is :

(Given, initial temperature of the bullet = 127°C, Melting point of the bullet = 327°C, Latent heat of fusion of lead $=2.5\times10^4$ J kg$^{-1}$, Specific heat capacity of lead = 125 J/kg K)

As per the given figure, two plates A and B of thermal conductivity K and 2 K are joined together to form a compound plate. The thickness of plates are 4.0 cm and 2.5 cm respectively and the area of cross-section is 120 cm$^2$ for each plate. The equivalent thermal conductivity of the compound plate is $\left(1+\dfrac5\alpha\right)$ K, then the value of $\alpha$ will be ______.

At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6.241 cm ? Both the diameters have been measured at room temperature (27°C).

(Given: coefficient of linear thermal expansion of gold $\alpha_L=1.4\times10^{-5}$ K$^{-1}$)

The pressure of the gas in a constant volume gas thermometer is 100 cm of mercury when placed in melting ice at 1 atm. When the bulb is placed in a liquid, the pressure becomes 180 cm of mercury. Temperature of the liquid is :

(Given 0°C = 273 K)