Heat & Thermodynamics — JEE Main PYQs

Three perfect gases at absolute temperatures $T_1,T_2$ and $T_3$ are mixed. The masses of molecules are $m_1$, $m_2$ and $m_3$ and the number of molecules are $n_1,n_2$ and $n_3$ respectively. Assuming no loss of energy, the final temperature of the mixture is …

A Carnot engine operating between temperatures $T_1$ and $T_2$ has efficiency $\frac{1}{6}$. When $T_2$ is lowered by 62 $K$, its efficiency increases to $\frac{1}{3}$. Then $T_1$ and $T_2$ are, respectively:

100 g of water is heated from $30^0\mathrm{C}$ to $50^0\mathrm{C}$. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is $4148\mathrm{J}/\mathrm{kg}/\mathrm{K}$) :

A diatomic ideal gas is used in a Car engine as the working substance. If during the adiabatic expansion part of the cycle, volume of the gas increases from V to 32 V the efficiency of the engine is

One kg of a diatomic gas is at a pressure of $8\times 10^4\mathrm{N}/{\mathrm{m}}^2$. The density of the gas is $4\mathrm{kg}/{\mathrm{m}}^{-3}$. What is the energy of the gas due to its thermal motion?

A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $\theta$ along the length x of the bar from its hot end is best described by which of the following figure.

Assuming the gas to be ideal the work done on the gas in taking it from A to B is

The work done on the gas in taking it from D to A is

The net work done on the gas in the cycle ABCDA is

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume ${\mathrm{V}}_1$ and contains ideal gas at pressure ${\mathrm{P}}_1$ and temperature ${\mathrm{T}}_1$. The other chamber has volume $V_2$ and contains ideal gas a …

One end of a thermally insulated rod is kept at a temperature $T_1$ and the other at $T_2$. The rod is composed of two sections of lengths ${\ell }_1$ and ${\ell }_2$ and thermal conductivities $k_1$ and $k_2$ respectively. The temperature at the interface of the two sectio …

If $C_p$ and $C_v$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then

When a system is taken from state i to state f along the path iaf, it is found that $\mathrm{Q}=50\mathrm{cal}$ and $\mathrm{W}=20\mathrm{cal}$. Along the path ibf $Q=36\mathrm{cal}$. W along the path ibf is

A Carnot engine, having an efficiency of $\eta =\frac{1}{10}$ as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is

Assuming the sun to be a spherical body of radius R at a temperature of T K, evaluate the total radiant power, incident on Earth, at a distance r from the Sun.

where $r_0$ is the radius of the Earth and $\sigma$ is Stefan's constant.

The work of 146 kJ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by $7^{\circ }\mathrm{C}$. The gas is
($\mathrm{R}=8.3\mathrm{J}{\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$)

Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature $T_0$, while Box B contains one mole of helium at temperature (7/3) $T_0$. The boxes are then put into thermal contact with each other and heat flows bet …

A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio $\frac{{\mathrm{C}}_{\mathrm{P}}}{{\mathrm{C}}_{\mathrm{v}}}$ of the mixture is

The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is

The figure shows a system of two concentric spheres of radii $r_1$ and $r_2$ and kept at temperatures $T_1$ and $T_2$ respectively. The radial rate of flow of heat in a substance between the two concentric sphere is proportional to

A system goes from A to B via two processes I and II as shown in the figure. If $\Delta {\mathrm{U}}_1$ and $\Delta {\mathrm{U}}_2$ are the changes in internal energies in the processes I and II respectively, the

One mole of ideal monoatomic gas ($\gamma =5/3$) is mixed with one mole of diatomic gas ($\gamma =7/5$). What is $\gamma$ for the mixture? $\gamma$ denotes the ratio of specific heat at constant pressure, to that at constant volume.

If the temperature of the sun were to increase from $T$ to $2T$ and its radius from $R$ to $2R$, then the ratio of the radiant energy received on earth to what it was previously will be

Which of the following statements is correct for any thermodynamic system?
(A) The internal energy changes in all processes.
(B) Internal energy and entropy are state functions.
(C) The change in entropy can never be zero.
(D) The work done in an adiabatic process is always zero.

Two thermally insulated vessels 1 and 2 are filled with air at temperatures $(T_1,T_2)$, volume $(V_1,V_2)$ and pressure $(P_1,P_2)$ respectively. If the valve joining two vessels is opened, the temperature inside the vessel at equilibrium will be

The temperature of two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x, respectively are $T_2$ and $T_1$ $(T_2>T_1)$. The rate of heat transfer through the slab, in a steady state …

Time taken by a 836 W heater to heat one litre of water from $10^{\circ }\text{C}$ to $40^{\circ }\text{C}$ is