Heat and Thermodynamics

If a gaseous mixture consists of 3 moles of oxygen and 4 moles of argon at an absolute temperature $T$, then the total internal energy of the mixture is (neglect vibrational modes and $R=$ Universal gas constant)

A monoatomic gas at a pressure of 100 kPa expands adiabatically such that its final volume becomes 8 times its initial volume. If the work done during the process is 180 J , then the initial volume of the gas is

The change in internal energy of given mass of a gas, when its volume changes from $V$ to $3 V$ at constant pressure $p$ is
( $\gamma=$ Ratio of the specific heat capacities of the gas)

The efficiency of a Carnot's heat engine is $\frac{1}{3}$. If the temperature of the source is decreased by $50^{\circ} \mathrm{C}$ and the temperature of the sink is increased by $25^{\circ} \mathrm{C}$, the efficiency of the engine become...

A rectangular slab consists of two cubes of copper and brass of equal sides having thermal conductivities in the ratio $4: 1$. If the free face of brass is at $0^{\circ} \mathrm{C}$ and that of copper is at $100^{\circ} \mathrm{C}$, then th...

When an ideal diatomic gas undergoes adiabatic expansion, if the increase in its volume is $0.5 \%$, then the change in the pressure of the gas is

To increase the rms speed of gas molecules by $25 \%$, the percentage increase in absolute temperature of the gas is to be

If some heat is given to a metal of mass 100 g , its temperature rises by $20^{\circ} \mathrm{C}$. If the same heat is given to 20 g of water, the change in its temperature (in ${ }^{\circ} \mathrm{C}$ ) is (The ratio of specific heat capac...

The ratio of the efficiencies of two Carnot engines $A$ and $B$ is 1.25 and the temperature difference between the source and the sink is same in both the engines. The ratio of the absolute temperature of the sources of the engines $A$ and ...

The heat supplied to a gas at a constant pressure of $5 \times 10^5 \mathrm{~Pa}$ is 1000 kJ . If the volume of gas changes from $1 \mathrm{~m}^3$ to $2.5 \mathrm{~m}^3$, then the change in internal energy of the gas is

If 5.6 litres of a monoatomic gas at STP is adiabatically compressed to 0.7 litres, then the work done on the gas is nearly ( $R=$ Universal gas constant)

If the ratio of universal gas constant and specific heat capacity at constant volume of a gas is given by 0.67 , then the gas is

If a body cools from a temperature of $62^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C}$ in 10 minutes and to $42^{\circ} \mathrm{C}$ in the next 10 minutes, then the temperature of the surroundings is

The internal energy of 4 moles of a monoatomic gas at a temperature of $77^{\circ} \mathrm{C}$ is
( $R=$ Universal gas constant)

If the rms speed of the molecules of a diatomic gas at a temperature of 322 K is $2000 \mathrm{~ms}^{-1}$, then the gas is (Universal gas constant $=8.31 \mathrm{Jmol}^{-1} \mathrm{~K}^{-1}$ )

A refrigerator of coefficient of performance 5 that extracts heat from the cooling compartment at the rate of 250 J per cycle is placed in a room. The heat released per cycle to the room by the refrigerator is

When 80 J of heat is supplied to a gas at constant pressure, if the work done by the gas is 20 J , then the ratio of the specific heat capacities of the gas is

The temperature of water of mass 100 g is rasied from $24^{\circ} \mathrm{C}$ to $90^{\circ} \mathrm{C}$ by adding steam to it. The mass of the steam added is
(Latent heat of steam $=540 \mathrm{cal} \mathrm{g}^{-1}$ and specific heat capac...

In a container of volume $16.62 \mathrm{~m}^3$ at $0{ }^{\circ} \mathrm{C}$ temperature, 2 moles of oxygen 5 moles of nitrogen and 3 moles of hydrogen are present, then the pressure in the container is
(Universal gas constant $=8.31 \mathrm...

If the given graph shows the logarithmic values of pressure ( $p$ ) and volume ( $V$ ) of an ideal gas, then the ratio of the specific heat capacities of the gas is

Steam at $100^{\circ} \mathrm{C}$ is passed into 114 g of water at $30^o$ The mass of water present in the mixture when the temperature of the water becomes $70^{\circ} \mathrm{C}$ is
(Latent heat of steam $=540 \mathrm{cal} \mathrm{g}^{-1}...

The internal energy of one mole of a rigid diatomic gas at absolute temperature $T$ is

In a Carnot engine if the work done during isothermal expansion is $25 \%$ more than the work done during isothermal compression, then the efficiency of the engine is

The work done to increase the volume of 2 moles of an ideal gas from V to 2 V at a constant temperature $T$ is W . The work to be done to increase the volume of 2 moles of the same gas from 2 V to 4 V at the same constant temperature $T$ is

If the internal energy of 3 moles of a gas at a temperature of $27^{\circ} \mathrm{C}$ is 2250 R , then the number of degrees of freedom of the gas is
( $R=$ Universal gas constant)

A small quantity of water of mass ' $m$ ' at temperature $\theta^{\circ} \mathrm{C}$ is mixed with a large mass ' $M$ ' of ice which is at its melting point. If ' $s$ ' is specific heat capacity of water and ' $L$ ' is the latent heat of fu...

If a heat engine and a refrigerator are working between the same two temperatures $T_1$ and $T_2\left(T_1>T_2\right)$, then the ratio of efficiency of heat engine to coefficient of performance of refrigerator is

The work done by 6 moles of helium gas when its temperature increases by $20^{\circ} \mathrm{C}$ at constant pressure is (Universal gas constant $=8.31 \mathrm{Jmol}^{-1} \mathrm{~K}^{-1}$ )

In a Carnot engine, if the absolute temperature of the source is $25 \%$ more than the absolute temperature of the sink, then the efficiency of the engine is

The fundamental limitation to the coefficient of performance of a refrigerator is given by

During adiabatic expansion, if the temperature of 3 moles of a diatomic gas decreases by $50^{\circ} \mathrm{C}$, then the work done by the gas is
( $R=$ Universal gas constant)

A Carnot heat engine absorbs 600 J of heat from a source at a temperature of $127^{\circ} \mathrm{C}$ and rejects 400 J of heat to a sink in each cycle. The temperature of the sink is

If the values of the temperature of a body in Fahrenheit and Celsius scales are in the ratio of $13: 5$, then the temperature of the body is

If the ratio of specific heats of a gas at constant pressure and at constant volume is $\gamma$, then the number of degrees of freedom of the rigid molecules of the gas is

A Carnot engine $A$ working between temperatures 600 K and $T(<600 \mathrm{~K})$ and another Carnot engine $B$ working between temperatures $T(>400 \mathrm{~K})$ and 400 K are connected in series. If the work done by both the engines is sam...

If the degrees of freedom of a gas molecule is 6 , then the total internal energy of the gas molecule at a temperature of $47^{\circ} \mathrm{C}$ (in eV ) is
(Boltzmann constant $=1.38 \times 10^{-23} \mathrm{JK}^{-1}$ )

When an ideal diatomic gas is heated at constant pressure, the fraction of the heat utilised to increase the internal energy of the gas is

Water of mass 5 kg in a closed vessel is at a temperature of $20^{\circ} \mathrm{C}$. If the temperature of the water when heated for a time of 10 minutes becomes $30^{\circ} \mathrm{C}$, then the increase in the internal energy of the wate...

If the wavelengths of maximum intensity of radiation emitted by two black bodies $A$ and $B$ are $0.5 \mu \mathrm{~m}$ and 0.1 mm respectively, then ratio of the temperatures of the bodies $A$ and $B$ is

The average translational kinetic energy of the oxygen molecules at a temperature of $127^{\circ} \mathrm{C}$ is
(Boltzmann constant $=1.38 \times 10^{-23} \mathrm{JK}^{-1}$ )

A gaseous mixture consists of 2 moles of oxygen and 4 moles of argon at an absolute temperature $T$. Neglecting all vibrational modes, the total internal energy of the mixture of the gases is

A Carnot engine having efficiency $60 \%$ receives heat from a source at a temperature 600 K . For the same sink temperature, to increase its efficiency to $80 \%$, then the temperature of the source is

If a gas of volume 400 cc at an initial pressure $p$ is suddenly compressed to 100 cc , then its final pressure is
(The ratio of the specific heat capacities of the gas at constant pressure and constant volume is 1.5 )

From the figure shown for a thermodynamic system, match the curves with their respective thermodynamic processes.
( $p=$ Pressure and $V=$ volume )
$$ \begin{array}{llll} \hline & \text { Curve } & & \text { Process } \\ \hline \text { (i) ...

An electric kettle takes 4 A current at 220 V . If the entire electric energy is converted into heat energy, then the time (in minutes) taken to increase the temperature of 1 kg of water from $34^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{...

If 2 moles of an ideal monoatomic gas at a temperature of $27^{\circ} \mathrm{C}$ is mixed with 4 moles of another ideal monoatomic gas at a temperature of $327^{\circ} \mathrm{C}$, then the temperature of mixture of the two gases is

If a refrigerator of coefficient of performance of 5 has a freezer at a temperature of $-13^{\circ} \mathrm{C}$, then the room temperature is

According to Zeroth law of thermodynamics, the physical quantity which is same for two bodies in thermal equilibrium is

The ratio of the molar specific heat capacities of monoatomic and diatomic gases at constant pressure is

A gas absorbs 18 J of heat and work done on the gas is 12 J . Then, the change in internal energy of the gas