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