Specific Heats

In a certain system of units, the fundamental unit of mass is taken as $2 \mathrm{kg},$ unit of length is taken as $\frac{1}{2} \mathrm{m},$ unit of time taken as $4 \mathrm{s}$ and unit of temperature is taken as $2$ Kelvin. In this system. $1$ unit of specific heat capacity will be (specific heat capacity is given by $s=\frac{Q}{m\times \Lambda T}.$ Where $Q$ is heat, $m$ is mass and $\Delta T$ is change in temperature) :-

Four different liquids, each of mass $1 \mathrm{kg}$, are separately heated at the same rate The initial temperatures of the liquids are all $20°\mathrm{C}$. The boiling points (b.p.), specific heat capacities (s.h.c.) and latent heat (L.h.) of the liquids are shown below. Which one of them will completely evaporate first?

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 $x$.

A $U$-tube, made of heat- insulating material, is shown in figure. One limb is closed by a non- conducting cork, the temperature is $T_0=300 K$. How much heat (in multiples of $100$ Joule) is required to be given by the coil so that the air rises to a temperature $T=510 K$? The thermal expansion of mercury is negligible. (Take:
Area of the tube as $0.1{ \mathrm{m}}^2,{\rho }_{\mathrm{Hg}}=13.6 \mathrm{g} {\mathrm{cc}}^{-1}; {\mathrm{P}}_{\mathrm{atm}}=75 \mathrm{cm}$ of $Hg,R=\frac{25}{3}$ SI units). Neglect the heat flow through the mercury.

A fuse made of a lead wire with a cross-section of $0.2{ \mathrm{mm}}^2$ is incorporated into a circuit of copper wire with a cross-section of $2{ \mathrm{mm}}^2$. On short circuiting the current reaches $30 A$. The temperature of wires before short circuiting is $T_0=20°\mathrm{C}$. Neglect the loss of heat due to thermal conductivity and radiation. Take the specific heat of lead and copper as constant and equal to $C_1=0.032\mathrm{cal} {\mathrm{gm}}^{-1}°\mathrm{C}$ and $C_2=0.091\mathrm{cal} {\mathrm{gm}}^{-1}°\mathrm{C}$ respectively. Given that resistivity and density of lead are ${\rho }_1=22\times {10}^{-6}\mathrm{ohm}-\mathrm{cm}$ and $d_1=11.34\mathrm{gm} {\mathrm{cm}}^{-3}$ and for copper ${\rho }_2=1.7\times {10}^{-6}\mathrm{ohm}-\mathrm{cm}$ and $d_2=8.9\mathrm{gm} {\mathrm{cm}}^{-3}$. The melting point of the lead is $T_1=327°\mathrm{C}$. Let  "$t_0$" is the time when the lead fuse begins to melt after the short circuit occurs and $\mathrm{\Delta }t$ is the rise in temperature of copper wire during this time. Then mark the CORRECT option(s) up to three significant figures after decimal

An ideal gas which undergoes through a process $V=a{T}^2;$ starting at $T_0$ and ends at $2T_0$. $a$ is a constant. The molar heat capacity of the gas if it is monoatomic is $\frac{n}{2}R$; What is $n$ ?

The SI unit of specific heat is $\raisebox{1ex}{$\mathrm{J}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{kg} \mathrm{K}$}\right.$.

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

The specific heat capacity of any substance is the amount of heat required to raise the temperature of one unit substance by hundred degree.

The amount of heat required to increase the temperature of one kilogram of a material, by $1 °\mathrm{C}$ is called latent heat.

The time taken for a calorimeter containing $75 \mathrm{g}$ of water at $62°\mathrm{C}$ to $\mathrm{cool}$ to $58°\mathrm{C}$ is $9$ minutes. When the calorimeter contains $105 \mathrm{g}$ of water, it takes $12$ minutes to cool from $62°\mathrm{C}$ to $58°\mathrm{C}$. The water equivalent of the calorimeter is

The specific heat capacity of water is less than that of steam.

The specific heat capacity of water is less than that of ice.

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}$}\right.$) 

The specific heat capacity of water is less than that of aluminium.

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, $s_w=4.2\times {10}^3 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$)

Explain the specific heat capacity of water.

A container has 4.2 litres of water at $40 {}^{°}\mathrm{C}$. Heat required to boil water in $\mathrm{kJ}$ is

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