Heat and Thermodynamics

A calorimeter of water equivalent 20 g contains 180 g of water at 25oC. ‘m’ grams of steam at
100oC is mixed in it till the temperature of the mixure is 31oC. The value of ‘m’ is close to :(Latent
heat of water = 540 cal g–1, specific heat ...

If minimum possible work is done by a refrigerator in converting 100 grams of water at 0oC to ice,
how much heat (in calories) is released to the surroundings at temperature 27oC (Latent heat of
ice = 80 Cal/gram) to the nearest integer ?

To raise the temperature of a certain mass of gas by 50oC at a constant pressure, 160 calories of
heat is required. When the same mass of gas is cooled by 100oC at constant volume, 240 calories
of heat is released. How many degrees of freed...

An engine takes in 5 moles of air at 20oC and
1 atm, and compresses it adiabatically to
1/10th of the original volume. Assuming air to
be a diatomic ideal gas made up of rigid
molecules, the change in its internal energy
during this process...

A gas mixture consists of 3 moles of oxygen
and 5 moles of argon at temperature T.
Assuming the gases to be ideal and the oxygen
bond to be rigid, the total internal energy (in
units of RT) of the mixture is :

When the temperature of a metal wire is
increased from 0oC to 10oC, its length
increases by 0.02%. The percentage change in
its mass density will be closest to :

A heat engine is involved with exchange of heat
of 1915 J, – 40J, + 125 J and –Q J, during one
cycle achieving an efficiency of 50.0%. The
value of Q is

An ideal gas in a closed container is slowly
heated. As its temperature increases, which of
the following statements are true?
(A) the mean free path of the molecules
decreases.
(B) the mean collision time between the
molecules decreases.
(...

A gas can be taken from A to B via two different processes ACB and ADB.

When path ACB is used 60 J of heat flows into the system and 30 J of work is done by the system. If path ADB is used work done by the system is 10 J. The heat Flow in...

Temperature difference of 120oC is maintained between ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and length \({{3L} \over 2},\) is connected across AB (see figure). In steady state, temperature ...

A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion \(\alpha\)/oC. It is observed that an external compressive force F, is applied on each of its ends, preve...

A mixture of 2 moles of helium gas (atomic mass = 4 u), and 1 mole of argon gas (atomic mass = 40 u) is kept at 300 K in a container. The ratio of their rms speeds \(\left[ {{{{V_{rms}}\,(helium)} \over {{V_{rms}}\,(\arg on)}}} \right],\) i...

A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature 27oC. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about : [Take R = 8.3 J/K mole]

Two Carnot engines A and B are operated in series. The first one, A, receives heat at T1 (= 600 K) and rejects to a reservoir at temperature T2. The second engine B receives heat rejected by the first engine and, in tum, rejects to a heat r...

For a given gas at 1 atm pressure, rms speed
of the molecule is 200 m/s at 127°C. At 2 atm
pressure and at 227°C, the rms speed of the
molecules will be :

Following figure shows two processes A and
B for a gas. If \(\Delta\)QA and \(\Delta\)QB are the amount of
heat absorbed by the system in two cases, and
\(\Delta\)UA and \(\Delta\)UB are changes in internal energies,
respectively, then ...

An HCl molecule has rotational, translational
and vibrational motions. If the rms velocity of
HCl molecules in its gaseous phase is \(\overline v\) , m is
its mass and kB is Boltzmann constant, then its
temperature will be :

A massless spring (k = 800 N/m), attached with
a mass (500 g) is completely immersed in 1 kg
of water. The spring is stretched by 2 cm and
released so that it starts vibrating. What would
be the order of magnitude of the change in the
tempe...

The specific heats, CP and CV of a gas of
diatomic molecules, A, are given (in units of
J mol–1 K–1) by 29 and 22, respectively.
Another gas of diatomic molecules, B, has the
corresponding values 30 and 21. If they are
treated as ideal gas...

Two materials having coefficients of thermal
conductivity '3K' and 'K' and thickness 'd' and
'3d', respectively, are joined to form a slab as
shown in the figure. The temperatures of the
outer surfaces are '\(\theta\)2' and '\(\theta\)1' ...

Two identical beakers A and B contain equal
volumes of two different liquids at 60°C each
and left to cool down. Liquid in A has density
of 8 × 102 kg/m3 and specific heat of
2000 J kg–1 K–1 while liquid in B has density
of 103 kg m–3 and s...

A thermally insulated vessel contains 150g of
water at 0°C. Then the air from the vessel is
pumped out adiabatically. A fraction of water
turns into ice and the rest evaporates at 0°C
itself. The mass of evaporated water will be
closest to ...

The given diagram shows four processes i.e.,
isochoric, isobaric, isothermal and adiabatic.
The correct assignment of the processes, in the
same order is given by :-

The temperature, at which the root mean square
velocity of hydrogen molecules equals their
escape velocity from the earth, is closest to :
[Boltzmann Constant kB = 1.38 × 10–23 J/K
Avogadro Number NA = 6.02 × 1026 /kg
Radius of Earth : 6.4 ...

An ideal gas occupies a volume of 2m3 at a pressure of 3 \(\times\) 106 Pa. The energy of the gas is :

A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is K1 and the of the outer cylinder is K2. Assuming no loss of heat, the effec...

For the given cyclic process CAB as shown for a gas, the work done is :

An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature 300 K. The mean time between two successive collisions is 6 \(\times\) 10–8 s. If the pressure is doubled and temperature is increased to 500 K, the mean time bet...

A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is \(\ell\)1, a...

At 40o C, a brass wire of 1 mm radius is hung from the ceiling. A small mass, M is hung from the free end of
the wire. When the wire is cooled down from 40oC to 20oC it regains its original length of 0.2 m. The value
of M is close to :
(Coe...

A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the
internal energy of the gas along the path ca is –180 J. The gas absorbs 250 J of heat along the path ab and 60
J along the path bc. ...

Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the
molar specific heat of mixture at constant volume ? (R = 8.3 J/mol K)

When M1 gram of ice at –10oC (specific heat = 0.5 cal g–1
oC–1
) is added to M2 gram of water at 50C, finally
no ice is left and the water is at 0°C. The value of latent heat of ice, in cal g–1
is :

One kg of water, at 20oC, heated in an electric kettle whose heating element has a mean (temperature
averaged) resistance of 20 \(\Omega\). The rms voltage in the mains is 200 V. Ignoring heat loss from the kettle, time
taken for water to ...

A diatomic gas with rigid molecules does 10 J of work when expanded at constant pressure. What would be
the heat energy absorbed by the gas, in this process ?

A Carnot engine has an efficiency of \({1 \over 6}\). When the temperature of the sink is reduced by 62ºC, its efficiency
is doubled. The temperatures of the source and the sink are, respectively

Ice at –20oC is added to 50 g of water at 40oC. When the temperature of the mixture reaches 0oC, it is found that 20 g of ice is still unmelted. The amount of ice added to the water was close to (Specific heat of water = 4.2J/g/oC Specific ...

A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume for this process is TVx = constant, then x is :

A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. considering only translational and rotational modes, the total internal energy of the system is :

Two rods A and B of identical dimensions are at temperature 30°C. If A is heated upto 180oC and B upto ToC, then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4 : 3, then the value of T is

A metal ball of mass 0.1 kg is heated upto 500oC and dropped into a vessel of heat capacity 800 JK–1 and containing 0.5 kg water. The initial temperature of water and vessel is 30oC. What is the approximate percentage increment in the tempe...

In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation VT = K, where K is a constant. In this process the temperature of the gas is increased by \(\Delta\)T. The
amount of heat abso...

When 100 g of a liquid A at 100oC is added to 50 g of a liquid B at temperature 75oC, the temperature of the mixture becomes 90oC. The temperature of the mixture, if 100 g of liquid A at 100oC is added to 50 g of liquid B at 50oC, will be :...

A thermometer graduated according to a linear scale reads a value x0 when in contact with boiling water, and x0/3 when in contact with ice. What is the temperature of an object in oC, if this thermometer in the contact with the object reads...

Three Carnot engines operate in series between a heat source at a temperature T1 and a heat sink at temperature T4 (see figure). There are two other reservoirs at temperature T2 and T3, as shown, with T1 > T2 > T3 > T4. The three engines ar...

A heat source at T = 103 K is connected to another heat reservoir at T = 102 K by a copper slab which is 1 mthick. Given that the thermal conductivity of copper is 0.1 WK–1m–1, the energy flux through it in the steady state is -

An unknown metal of mass 192 g heated to a temperature of 100oC was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of 8.4oC. Calculate the specific heat of the unknown metal if water temperature s...

Half mole of an ideal monoatomic gas is heated at constant pressure of 1 atm from 20oC to 90oC. Work done
by gas is close to – (Gas constant R = 8.31 J/mol.K)

Two kg of a monoatomic gas is at a pressure of 4 \(\times\) 104 N/m2. The density of the gas is 8 kg/m3. What is the order of energy of the gas due to its thermal motion ?

n moles of an ideal gas with constant volume
heat capcity CV undergo an isobaric expansion
by certain volume. The ratio of the work done
in the process, to the heat supplied is :