An ideal heat engine (Carnot engine) working between temperatures \(T_1\) and \(T_2\) has an efficiency \(\eta.\) The new efficiency if both the source and sink temperatures are doubled will be:
1. \(\frac{\eta}{2}\)
2. \(\eta\)
3. \(2\eta\)
4. \(3\eta\)

An engine is supposed to operate between two reservoirs at temperature 727°C and 227°C. The maximum possible efficiency of such an engine is -

(1) 1/2

(2) 1/4

(3) 3/4

(4) 1

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) $P_3>P_1,W>0$

(2) $P_3<P_1,W<0$

(3) $P_3>P_1,W<0$

(4) $P_3=P_1,W=0$

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:

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 \(T_1=800\) 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:

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