The molar heat capacity in the case of a diatomic gas if it does work of \(\dfrac{Q}{4}\) when heat \(Q\) is supplied to it is:
1. \(\dfrac{2}{5}R\)

2. \(\dfrac{5}{2}R\)

3. \(\dfrac{10}{3}R\)

4. \(\dfrac{6}{7}R\)

An insulator container contains 4 moles of an ideal diatomic gas at temperature T. Heat Q is supplied to this gas, due to which 2 moles of the gas are dissociated into atoms but temperature of the gas remains constant. Then

1. Q = 2RT

2. Q = RT

3. Q = 3RT

4. Q = 4RT

The volume of air increases by 5% in its adiabatic expansion. The percentage decrease in its pressure will be -

(1) 5%

(2) 6%

(3) 7%

(4) 8%

The temperature of a hypothetical gas increases to $\sqrt{2}$ times when compressed adiabatically to half the volume. Its equation can be written as

(1) PV^3/2 = constant

(2) PV^5/2 = constant

(3) PV^7/3 = constant

(4) PV^4/3 = constant

Two Carnot engines A and B are operated in succession. The first one, A receives heat from a source at T₁ = 800 K and rejects to sink at T₂ K. The second engine B receives heat rejected by the first engine and rejects to another sink at T₃ = 300 K. If the work outputs of two engines are equal, then the value of T₂ is -

(1) 100K

(2) 300K

(3) 550K

(4) 700K

When an ideal monoatomic gas is heated at constant pressure, fraction of heat energy supplied which increases the internal energy of gas, is 

(1) $\frac{2}{5}$

(2) $\frac{3}{5}$

(3) $\frac{3}{7}$

(4) $\frac{3}{4}$

When an ideal gas (γ = 5/3) is heated under constant pressure, then what percentage of given heat energy will be utilised in doing external work ?

1. 40 %

2. 30 %

3. 60 %

4. 20 %

Two samples A and B of a gas initially at the same pressure and temperature are compressed from volume V to V/2 (A isothermally and B adiabatically). The final pressure of A is 

(1) Greater than the final pressure of B

(2) Equal to the final pressure of B

(3) Less than the final pressure of B

(4) Twice the final pressure of B

Initial pressure and volume of a gas are P and V respectively. First it is expanded isothermally to volume 4V and then compressed adiabatically to volume V. The final pressure of gas will be [Given : $\gamma =1.5 ]$-

(1) 1P

(2) 2P

(3) 4P

(4) 8P

A thermally insulated rigid container contains an ideal gas heated by a filament of resistance 100 Ω through a current of 1A for 5 min . Then change in internal energy is -

(1) 0 kJ

(2) 10 kJ

(3) 20 kJ

(4) 30 kJ