Heat and Thermodynamics

If $C_p$ and $C_v$ are molar specific heats of an ideal gas at constant pressure and volume respectively and ' $\gamma$ ' is $\mathrm{C}_{\mathrm{p}} / \mathrm{C}_{\mathrm{v}}$ then $\mathrm{C}_{\mathrm{p}}=$
( $\mathrm{R}=$ universal gas c...

A lead bullet moving with velocity ' $v$ ' strikes a wall and stops. If $50 \%$ of its energy is converted into heat, then the increase in temperature is ( $s=$ specific heat of lead)

Two bodies ' X ' and ' Y ' at temperatures ' $\mathrm{T}_1$ ' K and ' $T_2$ ' K respectively have the same dimensions. If their emissive powers are same, the relation between their temperatures is

A pergect gas of volume 5 litre is compressed isothermally to volume of 1 litre. The r.m.s. speed of the molecules will

The change in the internal energy of the mass of gas, when the volume changes from ' $V$ ' to ' 2 V ' at constant pressure ' $P$ ' is ( $\gamma$ is the ratio of specific heat of gas at constant pressure to specific heat at constant volume)

A real gas behaves as an ideal gas at

Two spherical black bodies of radii ' $R_1$ ' and ' $\mathrm{R}_2$ ' and with surface temperature ' $\mathrm{T}_1$ ' and ' $\mathrm{T}_2$ ' respectively radiate the same power. The ratio of ' $R_1$ ' to ' $R_2$ ' will be

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

Given that ' $x$ ' joule of heat is incident on a body. Out of that, total heat reflected and transmitted is ' $y$ ' joule. The absorption coefficient of body is

Two rods, one of aluminium and the other of steel, having initial lengths ' $\mathrm{L}_1$ ' and ' $\mathrm{L}_2$ ' are connected together to form a single rod of length $\left(L_1+L_2\right)$. The coefficients of linear expansion of alumin...

There are two samples A and B of a certain gas, which are initially at the same temperature and pressure. Both are compressed from volume v to $\frac{\mathrm{v}}{2}$. Sample A is compressed isothermally while sample B is compressed adiabati...

The r.m.s. velocity of hydrogen at S.T.P. is ' $u$ ' $\mathrm{m} / \mathrm{s}$. If the gas is heated at constant pressure till its volume becomes three times, then the final temperature of the gas and the r.m.s. speed are respectively

The specific heat of argon at constant pressure and constant volume are $C_p$ and $C_v$ respectively. It's density ' $\rho$ ' at N.T.P. will be $[\mathrm{P}$ and T are pressure and temperature respectively at N.T.P.]

Two rods, one of copper ( Cu$)$ and the other of iron ( Fe ) having initial lengths $\mathrm{L}_1$ and $\mathrm{L}_2$ respectively are connected together to form a single rod of length $L_1+L_2$. The coefficient of linear expansion of Cu an...

A monoatomic gas is heated at constant pressure. The percentage of total heat used for doing external work is

A diatomic gas undergoes adiabatic change. Its pressure P and temperature T are related as $\mathrm{P} \propto \mathrm{T}^{\mathrm{x}}$ where the value of x is

The r.m.s. velocity of gas molecules kept at temperature $27^{\circ} \mathrm{C}$ in a vessel is $61 \mathrm{~m} / \mathrm{s}$. Molecular weight of gas is nearly
\(\left[\mathrm{R}=8.31 \frac{\mathrm{~J}}{\mathrm{~mol} \mathrm{~K}}\right]\)

A gas expands in such a way that its pressure and volume satisfy the condition $\mathrm{PV}^2=$ constant. Then the temperature of the gas

The frequency ' $v_{\mathrm{m}}$ ' corresponding to which the energy emitted by a black body is maximum may vary with the temperature ' $T$ ' of the body as shown by the curves ' A ', ' B ', ' C ' and ' D ' in the figure. Which one of these...

The P-V graph of an ideal gas, cycle is shown. The adiabatic process is described by the region

A sample of oxygen gas and a sample of hydrogen gas both have the same mass, same volume and the same pressure. The ratio of their absolute temperature is (Molecular wt. of $\mathrm{O}_2 & \mathrm{H}_2$ is 32 and 2 respectively)

One mole of an ideal gas at an initial temperature of ' $T$ ' $K$ does ' $6 R$ ' of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is $5 / 3$, the final temperature of gas will be ...

Railway track is made of steel segments separated by small gaps to allow for linear expansion. The segment of track is 10 m long when laid at temperature $17^{\circ} \mathrm{C}$. The maximum temperature that can be reached is $45^{\circ} \m...

At S.T.P., the mean free path of gas molecule is 1500 d , where ' $d$ ' is diameter of molecule. What will be the mean free path at 373 K at constant volume?

A fixed mass of gas at constant pressure occupies a volume ' V '. The gas undergoes a rise in temperature so that the r.m.s. velocity of the molecules is doubled. The new volume will be

The average translational kinetic energy of nitrogen (molar mass 28) molecules at a particular temperature is 0.042 eV . The translational kinetic energy of oxygen molecules (molar mass 32) in eV at double the temperature is

The first operation involved in a carnot cycle is

Rate of flow of heat through a cylindrical rod is ' $\mathrm{H}_1$ '. The temperature at the ends of the rod are ' $T_1$ ' and ' $T_2$ '. If all the dimensions of the rod become double and the temperature difference remains the same, the ra...

In an isobaric process

The temperature at which r.m.s. velocity of hydrogen molecules is 4.5 times that of an oxygen molecule at $47^{\circ} \mathrm{C}$ is (Molecular weight of hydrogen and oxygen molecules are 2 and 32 respectively)

In ideal gas of $27^{\circ} \mathrm{C}$ is compressed adiabatically to $(8 / 27)$ of its original volume. If $\gamma=\frac{5}{3}$, the rise in temperature of a gas is

An ideal diatomic gas is heated at constant pressure. What is the fraction of total energy applied, which increases the internal energy for the gas?

 A bucket full of hot water is kept in a room. If it cools from $75^{\circ} \mathrm{C}$ to $70^{\circ} \mathrm{C}$ in $t_1$ minutes, from $70^{\circ} \mathrm{C}$ to $65^{\circ} \mathrm{C}$ in $\mathrm{t}_2$ minutes and $65^{\circ} \mathrm{C...

The power radiated by a black body is P and it radiates maximum energy around the wavelength $\lambda_0$. Now the temperature of the black body is changed so that it radiates maximum energy around wavelength $\left(\frac{\lambda_0}{2}\right...

If heat energy $\Delta \mathrm{Q}$ is supplied to an ideal diatomic gas, the increase in internal energy is $\Delta U$ and the amount of work done by the gas is $\Delta \mathrm{W}$. The ratio $\Delta \mathrm{W}: \Delta \mathrm{U}: \Delta \m...

Assuming the expression for the pressure exerted by the gas, it can be shown that pressure is

The ratio of the specific heats $\frac{C_p}{C_v}=\gamma$, in terms of degrees of freedom ( n ) is

A monoatomic ideal gas is heated at constant pressure. The percentage of total heat used in changing the internal energy is

At certain temperature, $\operatorname{rod} \mathrm{A}$ and $\operatorname{rod} \mathrm{B}$ of different materials have lengths $\mathrm{L}_{\mathrm{A}}$ and $\mathrm{L}_B$ respectively. Their co-efficients of linear expansion are $\alpha_A...

Temperature remaining constant, the pressure of gas is decreased by $20 \%$. The percentage change in volume

The first operation involved in a Carnot cycle is

During an experiment, an ideal gas is found to obey an additional law $\mathrm{VP}^2=$ constant. The gas is initially at temperature ' T ' and volume ' V '. What will be the temperature of the gas when it expands to a volume 2 V ?

When a system is taken from state ' $a$ ' to state ' $c$ ' along a path abc, it is found that $\mathrm{Q}=80 \mathrm{cal}$ and $\mathrm{W}=35 \mathrm{cal}$. Along path adc $\mathrm{Q}=65 \mathrm{cal}$ the work done W along path adc is

The internal energy of an ideal diatomic gas corresponding to volume ' $V$ ' and pressure ' P ' is 2.5 PV. The gas expands from 1 litre to 2 litre at a constant pressure of $10^5 \mathrm{~N} / \mathrm{m}^2$. The heat supplied to a gas is

A sheet of steel is 40 cm long and 5 cm broad at $0^{\circ} \mathrm{C}$. The surface area of the sheet increases by $1.4 \mathrm{~cm}^2$ at $100^{\circ} \mathrm{C}$. Coefficient of linear expansion of steel is

The ratio of work done by an ideal rigid diatomic gas to the heat supplied by the gas in an isobaric process is

A quantity of heat ' $Q$ ' is supplied to monoatomic ideal gas which expands at constant pressure. The fraction of heat converted into work is $\left[\gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\frac{5}{3}\right]$

Four moles of hydrogen, two moles of helium and one mole of water vapour form an ideal gas mixture. $\left[C_{\mathrm{v}}\right.$ for hydrogen $=\frac{5}{2} R, C_v$ for helium $=\frac{3}{2} R, \quad C_{\mathrm{v}}$ for water vapour $\left.=...

A monoatomic ideal gas, initially at temperature $T_1$ is enclosed in a cylinder fitted with frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. $L_1$ and $L_2$ are the le...

The absolute temperature of a gas is determined by