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 of water = 1 cal g–1 oC–1)

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 freedom does each molecule of this gas have (assume gas to be ideal)?

Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature T is :

A balloon filled with helium (32oC and 1.7 atm.) bursts. Immediately afterwards the expansion of helium can be considered as

Three different processes that can occur in an ideal monoatomic gas are shown in the P vs V diagram. The paths are labelled as A $$\to$$ B, A $$\to$$ C and A $$\to$$ D. The change in internal energies during these process are taken as EAB, EAC and EAD and the work done as WAB, WAC and WAD. The correct relation between these parameters are :

Number of molecules in a volume of 4 cm3 of a perfect monoatomic gas at some temperature T and at a pressure of 2 cm of mercury is close to? (Given, mean kinetic energy of a molecule (at T) is 4 $$\times$$ 10–14 erg, g = 980 cm/s2, density of mercury = 13.6 g/cm3)

Two different wires having lengths L1 and L2, and respective temperature coefficient of linear expansion $$\alpha$$1 and $$\alpha$$2, are joined end-to-end. Then the effective temperature coefficient of linear expansion is :

In an adiabatic process, the density of a diatomic gas becomes 32 times its initial value. The final pressure of the gas is found to be n times the initial pressure. The value of n is :

Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom.The gas is maintained at a temperature of T. The total internal energy, U of a mole of this gas, and the value of \gamma \left( { = {{{C_p}} \over {{C_v}}}} \right) are given, respectively by:

In a dilute gas at pressure P and temperature T, the mean time between successive collisions of a molecule varies with T as :

Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity K1 , K2 and K3 , respecrtively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at 100oC and the other at 0oC (see figure). If the joints of the rod are at 70oC and 20oC in steady state and there is no loss of energy from the surface of the rod, the correct relationship between K1 , K2 and K3 is :

A carnot engine having an efficiency of {1 \over {10}} is being used as a refrigerator. If the work done on the refrigerator is 10 J, the amount of heat absorbed from the reservoir at lower temperature is :

A litre of dry air at STP expands adiabatically to a volume of 3 litres. If $$\gamma$$ = 1.40, the work done by air is : (31.4 = 4.6555) [Take air to be an ideal gas]

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

Two moles of an ideal gas with {{{C_P}} \over {{C_V}}} = {5 \over 3} are mixed with 3 moles of another ideal gas with {{{C_P}} \over {{C_V}}} = {4 \over 3}. The value of {{{C_P}} \over {{C_V}}} for the mixture is :

Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperature, T1 and T2 . The temperature of the hot reservoir of the first engine is T1 and the temperature of the cold reservoir of the second engine is T2 . T is temperature of the sink of first engine which is also the source for the second which is also the source for the second engine. How is T related to T1 and T2 . If both engines perform equal amount of work?

Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean collision time between the gas molecule changes from $${\tau }_1$$ to $${\tau }_2$$ . If {{{C_p}} \over {{C_v}}} = \gamma for this gas then a good estimate for {{{\tau _2}} \over {{\tau _1}}} is given by :

The plot that depicts the behavior of the mean free time t (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is: (Graphs are schematic and not drawn to scale)

A thermodynamic cycle xyzx is shown on a V-T diagram. The P-V diagram that best describes this cycle is : (Diagrams are schematic and not to scale)

Consider a mixture of n moles of helium gas and 2n moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its CP/CV value will be :