Specific Heat

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $\frac{C_{\mathrm{P}}}{C_{\mathrm{V}}}$  for the gas is $\frac{x}{2}$. Find $x$.

Two different liquids of same mass are kept in two identical vessel, which are placed in a freezer that extracts heat from them at the same rate causing each liquid to transform into a solid. The schematic figure below shows the temperaure $T$ vs time $t$ plot for the two materials. We denote the specific heat in the liquid states to be $C_{L1}$ and $C_{L2}$ for materials $1$ and $2$ respectively, and latent heats of fusion $U_1$ and $U_2$ respectively.

Choose the correct option.

Heat $\left(Q\right)$ is supplied to a solid to raise its temperature $\left(T\right)$ across its melting point $\left(T_M\right)$ and boiling point $\left(T_B\right).$ Which of the following graphs correctly represents the relation between heat supplied and temperature ?

200 g water is heated from ${40}^{\mathrm{ o}}\mathrm{C}$ to ${60}^{\mathrm{ o}}\mathrm{C}$ . Ignoring the slight expansion of water, the change in its internal energy is close to (Given specific heat of water $=4184$ J/kg/K):

A current carrying wire heats a metal rod. The wire provides a constant power $\left(\mathrm{P}\right)$ to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature $\left(\mathrm{T}\right)$ in the metal rod changes with time $\left(\mathrm{t}\right)$ as:

$\mathrm{T}\left(\mathrm{t}\right)={\mathrm{T}}_0\left(1+\mathrm{\beta }{\mathrm{t}}^{1/4}\right)$

where $\mathrm{\beta }$ is a constant with appropriate dimension while ${\mathrm{T}}_0$ is a constant with dimension of temperature. The heat capacity of the metal is:

A person weighing $50 \mathrm{kg}$ takes in $1500 \mathrm{kcal}$ diet per day. If this energy were to be used in heating the body of person without any losses, then the rise in his temperature is (specific heat of human body $=0.83 \mathrm{c}\mathrm{a}\mathrm{l}\mathrm{ }{\mathrm{g}}^{-1} {\mathrm{℃}}^{-1}$ )

Amongst object A and B, if the specific heat of object A is less than of object B, then 

Calorie is the unit of which physical quantity?

Calorie is the unit of which physical quantity?

What is the SI unit of heat?

A cube of lead of $500 \mathrm{g}$ at $25 °\mathrm{C}$ is supplied with a $3225 \mathrm{J}$ heat. Find the final temperature (in degree Celsius) of the lead cube. (Take, specific heat of lead is $0.129 \raisebox{1ex}{$\mathrm{J}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{g} °\mathrm{C}$}\right.$) 

Calculate the heat energy (in joules) to raise the temperature of $5 \mathrm{kg}$ of water from $20 °\mathrm{C}$ to $100 °\mathrm{C}$. (Take specific heat of water, $s_w=4.2\times {10}^3 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$)

The amount of heat required to raise the temperature of $1 \mathrm{kg}$ mass of water through $1 \mathrm{K}$ is called its

Specific heat of a substance is given by $S=(1+2T) \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$, find out amount of heat required to raise the temperature of $2 \mathrm{kg}$ substance from $10°\mathrm{C}$ to $20°\mathrm{C}.$

The number of degrees of freedom of a gas whose specific heat capacity at constant pressure is $33.24 \mathrm{J} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1},$ is
(universal gas constant $=8.31 \mathrm{J} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}$ )

The ends of a uniform metal rod of length $100 \mathrm{cm}$ and area of cross-section $2 {\mathrm{cm}}^2$ are maintained at $0 °\mathrm{C}$ and $100 °\mathrm{C}$. At the mid-point of the rod, heat is supplied at a constant rate of $40 \mathrm{J} {\mathrm{s}}^{-1}$. If the temperature gradient on the higher temperature side of the rod in steady state is $50x °\mathrm{C} {\mathrm{m}}^{-1}$, then the value of $x$ is (Thermal conductivity of the metal $=400 \mathrm{J} {\mathrm{s}}^{-1} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}$)

A copper wire $2 \mathrm{m}$ long is stretched by $1 \mathrm{mm}$. If the energy stored in the stretched wire is converted to heat, calculate the rise in temperature of the wire. (Given: $Y=12\times {10}^{11}$ $dyne {\mathrm{cm}}^{-2}$, Density of copper $=9 \mathrm{g} {\mathrm{cm}}^{-3}$ and Specific heat of copper $=0.1$ $cal\left.g^{-1} {}^{\circ }C^{-1}\right):$

$20 \mathrm{gm}$ ice at $-10°\mathrm{C}$ is mixed with $m \mathrm{gm}$ steam at $100°\mathrm{C}$. The minimum value of $\mathrm{m}$ so that finally all ice and steam converts into water is,

(Use, $s_{\text{ice}}=0.5 \mathrm{cal} {\mathrm{gm}}^{-1} °\mathrm{C}\text{,} s_{\text{water}}=1 \mathrm{cal} {\mathrm{gm}}^{-1} °\mathrm{C}$, $L$(melting)$=80 \mathrm{cal} {\mathrm{gm}}^{-1}$ and $L$ (vaporization)$=540 \mathrm{cal} {\mathrm{gm}}^{-1}$.)

Which statement is false for specific heat of water?