Heat and Thermodynamics

A black rectangular surface of area 'A' emits energy 'E' per second at $27^\circ$C. If length and breadth is reduced to half of its initial value and temperature is raised to $327^\circ$C then energy emitted per second becomes

The energy spectrum of a black body exhibits a maximum around a wavelength '$\lambda$'. The temperature of the black body is now changed such that the energy is maximum around a wavelength $2\lambda/3$. The power radiated by the black body ...

Rate of flow of heat through a cylindrical rod is '$H_1$'. 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 and if the rate of flow of...

If a gas is compressed isothermally then the r.m.s. velocity of the molecules

A rigid diatomic gas having molar mass m is contained in an insulated container. The container is moving with velocity V. If it is stopped suddenly, the change in temperature is (R - gas constant)

The average transnational kinetic energy of a molecule in a gas is $E_1$. The kinetic energy of the electron (e) accelerated from rest through potential difference 'V' volt is $E_2$. The temperature at which $E_1 = E_2$ possible is (mass of...

One gram of a liquid is converted to vapour at $3 \times 10^5$ Pa pressure. If 10% of the heat supplied is used for increasing the volume by $1600\ \text{cm}^3$ during this phase change, then the increase in internal energy in the process w...

A Carnot engine with efficiency 50% takes heat from a source at 600 K. To increase the efficiency by 20%, keeping temperature of the sink same, the new temperature of the source will be

A bowl filled with very hot water cools from $98^\circ\text{C}$ to $86^\circ\text{C}$ in 2 minutes when the room temperature is $22^\circ\text{C}$. How long it will take to cool from $75^\circ\text{C}$ to $69^\circ\text{C}$ ?

The average force applied on the walls of a closed container depends on temperature (T) as (T is the temperature of an ideal gas)

A monoatomic gas is stored in a thermally insulated container and the gas is suddenly compressed to $\left(\dfrac{1}{8}\right)^{th}$ of its initial volume. The ratio of final pressure to initial pressure is

In thermodynamic isobaric process

About black body radiation, which one of the following is a WRONG statement?

A black disc has a radius 'R' and wavelength corresponding to the maximum intensity is '$\lambda$'. The emissive power (E) for the different radii and maximum wavelengths is directly proportional to

An ordinary body cools from $4\theta$ to $3\theta$ in 't' minutes. The temperature of the body after next 't' minutes is (Assume Newton's law of cooling and room temperature as $\theta$)

An ideal gas is expanded adiabatically. How many times has the gas to be expanded to reduce the r.m.s. speed of molecules 3 times ? ($\gamma = 1.5$)

The average translational kinetic energy of a molecule in a gas is $E_1$. The kinetic energy of the electron (e) accelerated from rest through potential difference 'V' volt is $E_2$. The temperature at which $E_1 = E_2$ possible is (N = num...

In a cyclic process, work done by the system is

The energy spectrum of a black body exhibits a maximum around a wavelength $\lambda$. The temperature of a black body is now changed such that the energy is maximum at wavelength $2\lambda/3$. The power radiated by the black body will now i...

A black rectangular surface of area A emits energy E per second at $127^\circ$C. If length and breadth is reduced to half of initial value and temperature is raised to $527^\circ$C then energy emitted becomes

The ratio of the thermal conductivity of two rods of different materials is 6:5. The two rods of same area of cross section and same thermal resistance will have the length in the ratio

An ideal gas expands adiabatically ($\gamma = 1.5$). To reduce the r.m.s. velocity of the molecules 3 times the gas has to be expanded

The change in internal energy of the mass of gas, when the volume changes from V to 2V at constant pressure P is ($\gamma$ is the ratio of specific heat at constant pressure to that of volume) ($\gamma = \dfrac{C_p}{C_v}$)

A black rectangular surface of area A emits energy E per unit time at $27^\circ$ C. If length and breadth is reduced to $\left(\dfrac{1}{4}\right)^{th}$ of initial value and temperature is raised to $327^\circ$ C, then energy emitted per un...

Rate of radiation by a black body is 'R' at temperature 'T'. Another body has same area but emissivity is 0.2 and temperature 3T. Its rate of radiation is

A celsius and a Fahrenheit thermometer are dipped in boiling water. The temperature of water is lowered until the Farenheit thermometer shows $140^\circ$. What is the fall in temperature on the Celsius thermometer?

Let $\gamma_1$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a mono-atomic gas and $\gamma_2$ be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid ro...

According to law of equipartition of energy the molar specific heat of a non rigid diatomic gas at constant volume is

Energy of a gas/litre is $600$ joule, then what will be its pressure?

A sample of gas at temperature $T$ is adiabatically expanded to double its volume. The work done by the gas in the process is (given, $\gamma = \dfrac{3}{2}$):

The coefficient of thermal conductivity of a metal rod depends on its

What will be the ratio of rate of radiation of metal sphere at two different temperatures $T_1 = 527^\circ$C and $T_2 = 127^\circ$C

A vessel has $6$ gram of hydrogen at pressure $P$ and temperature $500$ K. A small hole is made in it so that hydrogen leaks out. How much hydrogen leaks out if the final pressure is $\dfrac{P}{2}$ and the temperature falls to $300$ K?

Two samples A and B of gas initially at the same pressure and temperature. They are compressed from volume $V$ to $\dfrac{V}{2}$ (A isothermally and B adiabatically). The relation between pressure of the gas A ($P_A$) and pressure of gas B ...

An ideal gas undergoes cyclic process ABCDA as shown in given p-V diagram. What is the magnitude of amount of work done by the gas?

The energy spectrum of a black body exhibits a maximum of wavelength $\lambda_0$. The temperature of the black body is now changed such that the energy is maximum at wavelength $\dfrac{3\lambda_0}{2}$. The ratio of power radiated by the bla...

A wire of length $L$ and diameter $d$ is used in a bulb. The temperature of wire is $T$ and power radiated by the wire is $P$. Its emissivity is ($\sigma$ = Stefan's constant) (Assume that emissivity of wire material is same at all waveleng...

Three identical heat conducting rods are connected in series as shown in the figure. The rods on the side have thermal conductivity $2K$ while that in the middle has thermal conductivity $K$. The left end of the combination is maintained at...

For a gas, $\dfrac{R}{C_v} = 0.4$ where R is the universal gas constant and $C_v$ is the molar specific heat at constant volume. The gas is made up of molecules which are

Carnot engine operating between temperatures $T_1$ and $T_2$ has efficiency $0.2$. When $T_2$ is lowered by $45$ K, its efficiency becomes $0.5$. Temperatures $T_1$ and $T_2$ are respectively

An insulated container contains a monoatomic gas of molar mass 'm'. The container is moving with velocity 'V'. If it is stopped suddenly, the change in temperature of the gas is (R-gas constant)

If $\Delta Q$ is the amount of heat supplied to 'n' moles of a rigid diatomic gas at constant pressure, $\Delta U$ is the change in internal energy and $\Delta W$ is the work done then $\Delta W : \Delta U : \Delta Q$ is

A rigid diatomic gas undergoes adiabatic change. Its pressure P and temperature T are related as $P \propto T^x$ where x is

A body cools in $7$ minutes from $60^\circ$C to $40^\circ$C. What time (in minutes) does it take to cool from $40^\circ$C to $28^\circ$C, if its surrounding temperature is $10^\circ$C ? (Newton's law of cooling holds good)

The outer surface of star in the form of a sphere radiates heat as a black body at temperature ' T '. The total radiant energy per unit area, normal to the direction of incidence, received at a distance ' $R$ ' from the centre of a star of ...

The relation between efficiency $(\eta)$ of Carnot engine and coefficient of performance $\left(\eta_1\right)$ of refrigerator is

A gas having $\gamma=\frac{5}{2}$ and volume 360 c.c. is suddenly compressed to 90 c.c. If the initial pressure of the gas is P , then the final pressure will be

A black body has maximum wavelength ' $\lambda_{\mathrm{m}}$ ' at temperature 2000 K . Its maximum wavelength at 3000 K will be

The length of steel rod is 5 cm longer than the copper rod at all temperatures. The length of the steel and copper rod is respectively (Coefficient of linear expansion for steel and copper is respectively $1.1 \times 10^{-5} /{ }^{\circ} \m...

500 gram of a diatomic gas is enclosed at a pressure of $10^5 \mathrm{Nm}^{-2}$. The density of the gas is $5 \mathrm{kgm}^{-3}$. The energy of one mole of the gas due to its thermal motion is [consider the gas molecule as a rigid rotator]