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

Which of the following processes is reversible ?

(1) Transfer of heat by radiation

(2) Electrical heating of a nichrome wire

(3) Transfer of heat by conduction

(4) Isothermal compression

A monoatomic ideal gas, initially at temperature T₁, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T₂ by releasing the piston suddenly. If L₁ and L₂ are the lengths of the gas column before and after expansion respectively, then T₁/ T₂ is given by -

(1) ${\left(\frac{{\displaystyle L_1}}{{\displaystyle L_2}}\right)}^{2/3}$

(2) $\frac{L_1}{L_2}$

(3) $\frac{L_2}{L_1}$

(4) ${\left(\frac{{\displaystyle L_2}}{{\displaystyle L_1}}\right)}^{2/3}$

A closed hollow insulated cylinder is filled with gas at \(0^{\circ}\mathrm{C}\) and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to \(100​​^{\circ}\mathrm{C}\). If the piston moves 5 cm, the length of the hollow cylinder will be:
1. 13.65 cm
2. 27.3 cm
3. 38.6 cm
4. 64.6 cm

A monoatomic gas is supplied with the heat \(Q\) very slowly, keeping the pressure constant. The work done by the gas will be: 
1. \({2 \over 3}Q\)
2. \({3 \over 5}Q\)
3. \({2 \over 5}Q\)
4. \({1 \over 5}Q\)

An ideal gas expands isothermally from a volume \(V_1\) to \(V_2\) and then is compressed to the original volume \(V_1\) adiabatically. The initial pressure is \(P_1\) and the final pressure is \(P_3.\) 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. \(𝑃 _3 = 𝑃 _1 ,    𝑊 = 0\)

Work done by a system under isothermal change from a volume V₁ to V₂ for a gas which obeys Vander Waal's equation $(V-\beta n)\left(P+\frac{{\displaystyle \alpha n^2}}{{\displaystyle V}}\right)=nRT$

(1) $nRT{\log }_e\left(\frac{{\displaystyle V_2-n\beta }}{{\displaystyle V_1-n\beta }}\right)+\alpha n^2\left(\frac{{\displaystyle V_1-V_2}}{{\displaystyle V_1{V}_2}}\right)$

(2) $nRT{\log }_{10}\left(\frac{{\displaystyle V_2-\alpha \beta }}{{\displaystyle V_1-\alpha \beta }}\right)+\alpha n^2\left(\frac{{\displaystyle V_1-V_2}}{{\displaystyle V_1{V}_2}}\right)$

(3) $nRT{\log }_e\left(\frac{{\displaystyle V_2-n\alpha }}{{\displaystyle V_1-n\alpha }}\right)+\beta n^2\left(\frac{{\displaystyle V_1-V_2}}{{\displaystyle V_1{V}_2}}\right)$

(4) $nRT{\log }_e\left(\frac{{\displaystyle V_1-n\beta }}{{\displaystyle V_2-n\beta }}\right)+\alpha n^2\left(\frac{{\displaystyle V_1{V}_2}}{{\displaystyle V_1-V_2}}\right)$

A cylindrical tube of uniform cross-sectional area A is fitted with two air tight frictionless pistons. The pistons are connected to each other by a metallic wire. Initially the pressure of the gas is P₀ and temperature is T₀, atmospheric pressure is also P₀. Now the temperature of the gas is increased to 2T₀, the tension in the wire will be

(1) 2 P₀A

(2) P₀A

(3) $\frac{P_{0}A}{2}$

(4) 4 P₀A