# Thermodynamics and Statistical Physics [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 28 - 31 of 82

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## Question 28

Appeared in Year: *2011*

### Question

MCQ▾A system has two energy levels with energies and . The lower level is fold degenerate while the upper level is doubly degenerate. If there are N non – interacting classical particles in the system, which is in thermodynamic equilibrium at temperature , the fraction of particles in the upper level is

### Choices

Choice (4) | Response | |
---|---|---|

a. | ||

b. | ||

c. | ||

d. |

## Question 29

Appeared in Year: *2013*

### Question

MCQ▾A proton is confined to a cubic box, whose sides have length . What is the minimum kinetic energy of the proton? The mass of proton is and Planck՚s constant is –

### Choices

Choice (4) | Response | |
---|---|---|

a. | ||

b. | ||

c. | ||

d. |

## Question 30

Appeared in Year: *2013*

### Question

MCQ▾Across a first order phase transition, the free energy is –

### Choices

Choice (4) | Response | |
---|---|---|

a. | Proportional to the temperature | |

b. | A continuous function of the temperature but its derivative is discontinuous | |

c. | Such that the first derivative with respect to temperature is continuous | |

d. | A discontinuous function of the temperature |

## Question 31

Appeared in Year: *2013*

### Question

MCQ▾The entropy function of a system is given by , where and are positive constants. The temperature of the system is –

### Choices

Choice (4) | Response | |
---|---|---|

a. | Negative for some energies | |

b. | Decreases monotonically with energy | |

c. | Zero | |

d. | Increases monotonically with energy |