Specific Heat

A metal ball of mass $0.1 \mathrm{kg}$ is heated upto $500 °\mathrm{C}$ and dropped into a vessel of heat capacity $800 \mathrm{J} {\mathrm{K}}^{-1}$ and containing $0.5 \mathrm{kg}$ water. The initial temperature of water and vessel is $30 °\mathrm{C}$. What is the approximate percentage increment in the temperature of the water? [Take specific heat capacities of water and metal are, respectively, $4200 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$ and $400 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$]

When $100 \mathrm{g}$ of a liquid $A$ at $100 °\mathrm{C}$ is added to $50 \mathrm{g}$ of a liquid $B$ at temperature $75 °\mathrm{C},$ the temperature of the mixture becomes $90 °\mathrm{C}$. The temperature of the mixture, if $100 \mathrm{g}$ of liquid $A$ at $100 °\mathrm{C}$ is added to $50 \mathrm{g}$ of liquid $B$ at $50 °\mathrm{C}$ will be

An unknown metal of mass $192 \mathrm{g}$ heated to a temperature of $100 °\mathrm{C}$ was immersed into a brass calorimeter of mass $128 \mathrm{g}$ containing $240 \mathrm{g}$ of water at a temperature of $8.4°\mathrm{C}$. Calculate the specific heat of the unknown metal, if water temperature stabilises at $21.5 °\mathrm{C}$. (Take, the specific heat of brass is $394 \mathrm{J} {\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$)

Two identical beakers $A$ and $B$ contain equal volumes of two different liquids at $60 °\mathrm{C}$ each and left to cool down. Liquid in $A$ has density of $8\times {10}^2 \mathrm{kg} {\mathrm{m}}^{-3}$ and specific heat of $2000 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$ while liquid in $B$ has density of ${10}^3 \mathrm{kg}$ ${\mathrm{m}}^{-3}$ and specific heat of $4000 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$. Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same)

In a reversible ideal engine, $650 \mathrm{J}$ of heat comes from the source of $450 \mathrm{K}$, heat rejected to sink at $225 \mathrm{K}$ is

Two spherical black bodies of radii $r_1$ and $r_2$ and with surface temperatures $T_1$ and $T_2$ respectively, radiate the same power. Then, the ratio of $r_1$ and $r_2$ will be

$A,B$ and $C$ are three identical conductors but made from different materials. They are kept in contact as shown. Their thermal conductivities are $K, 2K$ and $\frac{K}{2}$ respectively. The free end of $A$ is at $100°\mathrm{C}$ and the free end of $C$ is at $0°\mathrm{C}$. During steady-state, the temperature of the junction of $A$ and $B$ is nearly

If a piece of metal is heated to temperature $\theta$ and then allowed to cool in a room which is at temperature ${\theta }_0$. The graph between the temperature $T$ of the metal and time $t$ will be closed to

Two rectangular blocks, having identical dimensions, can be arranged either in the configuration $1$ or in configuration $2$ as shown in the figure. One of the blocks has thermal conductivity $K$ and the other $2K$. The temperature difference between the ends along the $x$ -axis is the same in both the configurations. It takes $9$ $\mathrm{s}$ to transport a certain amount of heat from the hot end to the cold end in the configuration $1$. The time to transport the same amount of heat in the configuration $2$ is

The same quantity of ice is filled in each of the two metal containers $P$ and $Q$ having the same size, shape and wall thickness but made of different materials. The containers are kept in identical surroundings. The ice in $P$ melts completely in time $t_1$ whereas in $Q$ takes a time $t_2$. The ratio of thermal conductivities of the materials of $P$ and $Q$ is

Consider black body radiation in a cubical box at absolute temperature $T$. If the length of each side of the box is doubled and the temperature of the walls of the box and that of the radiation is halved, then the total energy

Three rods of copper, brass and steel are welded together to form a $Y$-shaped structure. Area of a cross-section of each rod is $4 {\mathrm{cm}}^2$. End of the copper rod is maintained at $100°\mathrm{C}$ whereas ends of brass and steel are kept at $0°\mathrm{C}$. Lengths of the copper, brass and steel rods are $46 \mathrm{cm}$, $13 \mathrm{cm}$, and $12 \mathrm{cm}$ respectively. The rods are thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are$0.92, 0.26$ and $0.12$ in $CGS$ units, respectively. Rate of heat flow through copper rod is

Assertion: Snow is a better insulator than ice.
Reason: Snow contains air packet and the air is a good insulator of heat.

Assertion: Blue star is at high temperature than a red star.

Reason: Wien's displacement law states that, $T\propto \left(\frac{1}{{\lambda }_{\mathrm{m}}}\right)$

Assertion: It is hotter over the top of fire than at the same distance on the sides.

Reason: Air surrounding the fire conducts more heat upwards.

Assertion: For higher temperature, the peak emission wavelength of a black body shifts to lower wavelengths.
Reason: Peak emission wavelength of a blackbody is proportional to the fourth power of temperature.

Assertion: A body that is a good radiator is also a good absorber of radiation at a given wavelength.

Reason: According to Kirchhoff's law, the absorptivity of a body is equal to its emissivity at a given wavelength.

Ice formed over lakes

Two thin blankets keep more hotness than one blanket of thickness equal to these two. The reason is

The length of the two rods made up of the same metal and having the same area of cross-section are $0.6 \mathrm{m}$ and $0.8 \mathrm{m}$, respectively. The temperature between the ends of the first rod is $90°\mathrm{C}$ and $60°\mathrm{C}$ and that for the other rod is $150°\mathrm{C}$ and $110°\mathrm{C}$. For which rod the rate of conduction will be greater?