Heat and Thermodynamics

Gas at pressure P, temperature T, and volume V is filled in jar A. Another jar B is filled with gas having parameters $2P$, $\dfrac{V}{4}$, $2T$. The ratio of number of molecules of jar B to those of jar A is

An ideal rigid diatomic gas $\left(\gamma = \dfrac{7}{5}\right)$ undergoes an adiabatic change . If the relation between temperature and volume is $TV^x = $ constant then the value of x is

A rigid diatomic gas $\left(\gamma = \dfrac{7}{5}\right)$ is compressed adiabatically to volume $\left(\dfrac{V_i}{32}\right)$, where $V_i$ is the initial volume. The initial temperature of the gas is '$T_i$' K and the final temperature is ...

Two rods of same length, radius and material transfer a given amount of heat in 't' second when they are joined as shown in fig (1). But when they are joined as shown in fig (2) then they will transfer same heat in same condition in time

A sphere is at temperature $600$ K. In an external environment of $200$ K, its cooling rate is R. When the temperature of the sphere falls to $400$ K then cooling rate R' will become

An ideal gas having pressure $P$, volume $V$ and temperature $T$ is expanded isothermally, to a volume $3V$ and final pressure $P_I$. The same gas is expanded adiabatically to a volume $3V$, the final pressure being $P_A$. The ratio $\dfrac...

The efficiency of Carnot engine which operates between the two temperatures $T_1 = 500$ K and $T_2 = 300$ K is

A black body is at temperature of 5780 K. The energy of radiation emitted by the body at wavelength 300 nm is $U_1$, at wavelength 500 nm is $U_2$ and that at 900 nm is $U_3$ respectively. Wien's constant $b = 2.89 \times 10^6\ \text{nmK}$....

A sphere having temperature 600 K is losing heat due to radiation. At this temperature its rate of cooling is $R$. The rate of cooling of this sphere at 400 K is $\dfrac{x}{243}$. The value of $x$ is (Temperature of surrounding is 300 K)

A piece of metal of 850 K is dropped into 1 kg of water at 300 K. If equilibrium temperature of water is 350 K then the heat capacity of the metal expressed in $\dfrac{J}{K}$ is $\left(\text{Sp. heat of water} = 1\ \dfrac{\text{cal}}{\text{...

Two stars A and B radiate maximum energy at wavelength $3.9 \times 10^{-7}$ m and $5.2 \times 10^{-7}$ m respectively. The ratio of the temperature of star A to that of star B will be

The kinetic energy of an ideal gas is $E_0$ at $27^\circ\text{C}$. When the temperature is increased to $177^\circ\text{C}$, then kinetic energy will be

The thermodynamic process in which no work is done by the gas or on the gas is

A gas at normal temperature is suddenly compressed to one-fourth of its original volume. If $\gamma = 1.5$, then the increase in the temperature of the gas in Kelvin is ($\gamma$ is the ratio of specific heats)

If the two temperatures on Fahrenheit scale differ by $54^\circ\text{F}$, then the difference in temperature on the Celsius scale is

A black body is at temperature $827^\circ\text{C}$. The rate at which it emits energy is proportional to

When $170$ J of energy is incident on a surface of a body, $17$ J of energy is reflected by it. If the coefficient of absorption is $0.7$, then the amount of energy transmitted will be

An ideal gas ($\gamma = 1.5$) is expanded adiabatically. To reduce the root mean square velocity of molecules two times, the gas should be expanded

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

An ideal gas at pressure 'P' and temperature 'T' is enclosed in a vessel of volume 'V'. Some gas leaks through a hole from the vessel and the pressure of the enclosed gas falls to $P^1$. Assuming that the temperature of the gas remains cons...

An ideal gas having pressure P, volume V and temperature T undergoes a thermodynamic process in which $dW = 0$ and $dQ < 0$. Then, for the gas

$15$ g of ice at $0^\circ\text{C}$ is added to a vessel containing water at $40^\circ\text{C}$. The mass of water and water equivalent of the vessel is $60$ g. Assuming that negligible heat is taken from the surroundings, the final temperat...

Out of the following, which statement is NOT true about black body radiation ?

An ideal gas is heated from $27^\circ\text{C}$ to $627^\circ\text{C}$ at constant pressure. If initial volume of gas is $4\ \text{m}^3$, then the new volume of the gas will be

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

Which of the following graphs between pressure and volume of a gas correctly shows isochoric process in thermodynamics?

In thermodynamic process for free expansion, select the 'WRONG' statement out of the following options.

The ratio of thermal conductivity of two rods of different materials is $4:3$. The two rods have same area of cross-section and same thermal resistance. The lengths of rods are in the ratio

Two spherical black bodies of radii $R_1$ and $R_2$ having surface temperature $T_1$ and $T_2$ respectively, radiate the same power. The ratio of $R_1$ to $R_2$ will be

When the r.m.s. velocity of a gas is denoted by '$v$' at temperature '$T$'. Out of the following relations, the true one is

At a pressure P and temperature T, 7 gram of oxygen occupies a volume V. The equation of state will be (Molecular weight of Oxygen $= 32$)

An ideal gas with pressure P, volume V and temperature T is expanded isothermally to volume 2V and a final pressure $P_i$. The same gas is expanded adiabatically to a volume 2V then the final pressure is $P_a$. In terms of $\gamma$, the rat...

An ideal monoatomic gas is taken around the cycle ABCDA as shown in the P.V diagram. The work done during the cycle is

A body cools from a temperature $3\theta$ to $2\theta$ in 10 minute. The room temperature is $\theta$. The temperature of the body at the end of the next 10 minute is '$x$'. Assuming that Newton's law of cooling is applicable, the value of ...

A black body radiates maximum energy at wavelength '$\lambda$' at temperature $T_1$ and its emissive power is E. When the temperature of the body is changed to $T_2$, it radiates maximum energy at wavelength $\dfrac{2\lambda}{3}$, then the ...

The speeds of the seven molecules are 1, 3, 5, 7, 2, 4 and 6 km/s respectively. The ratio of their r.m.s. velocity and average velocity will be

The heat energy that must be supplied to 14 g of nitrogen at room temperature to raise its temperature by $48\ ^\circ\text{C}$ at constant pressure is ($R$ = gas constant, Molecular weight of nitrogen $(\text{N}_2)$ = 28)

A Carnot engine, whose efficiency is 40% takes heat from a source maintained at temperature 600K. To have an efficiency 60%, the intake temperature for the same exhaust temperature should be

Consider two rods 1 and 2 of same length. They have different specific heats $(C_1, C_2)$, thermal conductivities $(K_1, K_2)$ and area of cross-section $(A_1, A_2)$ respectively. Both the rods have temperatures $(T_1, T_2)$ at their ends. ...

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

In an external environment of temperature ($T$) kelvin, a sphere at temperature ($3T$) kelvin has cooling rate $R_1$. When the temperature of that sphere falls to ($2T$) kelvin, the cooling rate $R_2$ of the sphere will become

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

Two cylinders A and B fitted with pistons contain equal amount of an ideal diatomic gas at 303 K. The piston of cylinder A is free to move and that of cylinder B is held fixed. The same amount of heat is given to the gas in each cylinder. I...

A thermodynamic system is compressed adiabatically, then its temperature

A carnot engine having efficiency $\dfrac{1}{6}$, operates between the source temperature $T_H$ and the sink temperature $T_C$. Its efficiency increases to $\dfrac{1}{3}$, when $T_C$ is decreased by 64 K. The temperatures $T_H$ and $T_C$ ar...

In a composite slab there are two materials having coefficients of thermal conductivity K and 2K, thickness x and 4x repectively. The temperature of the two outer surfaces of a composite slab are $T_2$ and $T_1$ $(T_2 > T_1)$. $T_2$ is on s...

A black body emits radiation of maximum intensity of wavelength '$\lambda$' at temperature 'T' K. Its corresponding wavelength at temperature $(2.5T)$ K will be

The translational kinetic energy of the molecules of a gas at absolute temperature (T) can be doubled by

An ideal gas at $27^\circ$C is compressed adiabatically to $\left(\dfrac{8}{27}\right)$ of its original volume. If $\gamma = 5/3$, then the rise in temperature of a gas is

A monoatomic gas at pressure P having volume V expands isothermally to a volume 3V and then adiabatically to a volume 81 V. The final pressure of the gas is ($\gamma = 5/3$).