An ideal gas heat engine operates in Carnot cycle between 227°C and 127°C. It absorbs 6 × 104 cal of heat at higher temperature. Amount of heat converted to work is -
(1) 2.4 × 104 cal
(2) 6 × 104 cal
(3) 1.2 × 104 cal
(4) 4.8 × 104 cal
A monoatomic ideal gas, initially at temperature \(T_1\), is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature \(T_2\) by releasing the piston suddenly. If \(L_1\) and \(L_2\) are the lengths of the gas column before and after expansion, respectively, then \(\frac{T_1}{T_2}\) is given by:
1. \(\left(\frac{L_1}{L_2}\right)^{\frac{2}{3}}\)
2. \(\frac{L_1}{L_2}\)
3. \(\frac{L_2}{L_1}\)
4. \(\left(\frac{L_2}{L_1}\right)^{\frac{2}{3}}\)
An ideal gas expands isothermally from a volume V1 to V2 and then compressed to original volume V1 adiabatically. Initial pressure is P1 and final pressure is P3. The total work done is W. Then -
(1)
(2)
(3)
(4)
An insulator container contains 4 moles of an ideal diatomic gas at a temperature T. If heat Q is supplied to this gas, due to which 2 moles of the gas are dissociated into atoms, but the temperature of the gas remains constant, then:
1. Q = 2RT
2. Q = RT
3. Q = 3RT
4. Q = 4RT
The volume of air (diatomic) increases by \(5\%\) in its adiabatical 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 times when compressed adiabatically to half the volume. Its equation can be written as
(1) PV3/2 = constant
(2) PV5/2 = constant
(3) PV7/3 = constant
(4) PV4/3 = constant
Two Carnot engines A and B are operated in succession. The first one, A receives heat from a source at \(T_1=800\) K and rejects to sink at \(T_2\) K. The second engine, B, receives heat rejected by the first engine and rejects to another sink at \(T_3=300\) K. If the work outputs of the two engines are equal, then the value of \(T_2\) will be:
1. | 100 K | 2. | 300 K |
3. | 550 K | 4. | 700 K |
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
The 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 the gas will be: [Given: \(\gamma = 1.5\)]
1. | \(P\) | 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