Specific Heat Capacity

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.

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):

Water is used as a coolant because 

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 

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

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 $=8.31 \mathrm{J} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}$ )

$20 \mathrm{gm}$ 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?

During illness an $80 \mathrm{kg}$ man ran a fever of $102.2 °\mathrm{F}$ instead of normal body temperature of $98.6 °\mathrm{F}.$ Assuming that the human body is mostly water, how much heat is required to raise his temperature by that amount?

A source of heat supplies heat at a constant rate to a solid cube. The slope of portion $\mathrm{CD}$ of the graphs gives :-

For next 2 question please follow the same

Molar heat capacity of an ideal gas in the process $P{V}^x =$ constant is given by

             $\text{C}=\frac{\text{R}}{\text{γ}-1}+\frac{\text{R}}{1-\text{x}}$

An ideal diatomic gas with ${\text{C}}_{\text{V}}=\frac{5\text{R}}{2}$  occupies a volume V₁ at a pressure P₁ . The gas undergoes a process in which the pressure is proportional to the volume. At the end of the process the rms speed of the gas molecules has doubled from its initial value.

The molar heat capacity of the gas in the given process is

When $0.2 \mathrm{kg}$ of brass at $100°\mathrm{C}$ is dropped into $0.5 \mathrm{kg}$ of water at $20 °\mathrm{C},$ the resulting temperature is $23°\mathrm{C}$. What must have been the specific heat of brass ?
$\left(\text{Specific heat of water is}, s=4200 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}\right)$

In a mixture of two gases, we have $1$ mole of a certain gas having $\gamma =\frac{7}{5}$ and $1$ mole of another gas having $\gamma =\frac{4}{3}$. Calculate the value of $\gamma$ for the given mixture of gases.

Water is used as a coolant because 

An electric heater supplies $1.8 \mathrm{k}\mathrm{W}$ of power in the form of heat to a tank of water. How long will it take to heat $100 \mathrm{k}\mathrm{g}$ of water in the tank from $10$ to ${70}^o\mathrm{C}.$ Assume heat loss to the surrounding to be negligible.