The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is

• 1/2

• 1/4

• 1/3

• 1/3

A system goes from A to B via two processes I and II as shown in the figure. If ∆U₁ and ∆U₂ are the changes in internal energies in the processes I and II respectively, the

• ∆U₁ = ∆U₂

• relation between ∆U₁ and ∆U₂ can not be determined

• ∆U₂ > ∆U₁

• ∆U₂ > ∆U₁

Which of the following statements is correct for any thermodynamic system?

• The internal energy changes in all processes.

• Internal energy and entropy are state functions.

• The change in entropy can never be zero.

• The change in entropy can never be zero.

24.

Two thermally insulated vessels 1 and 2 are filled with air at temperatures (T₁, T₂), volume (V₁, V₂) and pressure (P₁, P₂) respectively. If the valve joining two vessels is opened, the temperature inside the vessel at equilibrium will be

• T₁ + T₂

• T₁ + T₂/2

• 
• 

Two moles of an ideal monoatomic gas occupies a volume V at 27°C. The gas expands adiabatically to a volume 2 V. Calculate (a) the final temperature of the gas and (b) change in its internal energy.

• (a) 195 K (b) 2.7 kJ

• (a) 189 K (b) 2.7 kJ

• (a) 195 K (b) –2.7 kJ

• (a) 189 K (b) – 2.7 kJ

Match the following

• I-4, II-3, III-2, IV-1

• I-3, II-2, III-1, IV-4

• I-1, II-2, III-3, IV-4

• I-4, II-2, III-3, IV-1

The Zeroth law of thermodynamics leads to the concept of

• internal energy

• heat content

• pressure

• temperature

The Carnot cycle of a reversible heat engine consists of

• one isothermal and two adiabatic processes

• two isothermal and one adiabatic processes

• two isothermal and two adiabatic processes

• two isobaric and two isothermal processes

A rigid container with thermally insulated walls contains a gas and a coil of resistance 50 Ω, carrying a current of 1 A. The change in internal energy of the gas after 2 min will be

• 6 kJ

• 10 kJ

• 3 kJ

• 12 kJ

Two soap bubbles each with radius r₁ and r₂ coalesce in vacuum under isothermal conditions to form a bigger bubble of radius R. Then, R is equal to

• $\sqrt{{{\mathrm{r}}_1}^2 + {{\mathrm{r}}_2}^2}$

• $\sqrt{{{\mathrm{r}}_1}^2 - {{\mathrm{r}}_2}^2}$

• r₁ + r₂

• $\frac{\sqrt{{{\mathrm{r}}_1}^2 + {{\mathrm{r}}_2}^2}}{2}$