Specific heat capacities:

copper | 400Jkg^{-1}K^{-1} | |

iron | 460Jkg^{-1}K^{-1} | |

water | 4200Jkg^{-1}K^{-1} | |

ice | 2100Jkg^{-1}K^{-1} |

Specific latent heat of fusion of ice = 3·3×10

^{5}Jkg^{-1}
Molar heat capacities of a diatomic ideal gas:

C

C

_{v}= 12·5J(molK)^{-1}and C_{p}= 20·8J(molK)^{-1}**Question 11**

Explain briefly a) why a gas exerts a pressure and b) why the pressure increases with temperature. |

**Question 12**

Two cylinders (of negligible heat capacity) each contain 1mol of a gas. The gas in each cylinder is supplied with enough heat to increase its temperature by 1K. One cylinder is heated at constant volume and the other is heated at constant pressure. By considering the quantities of heat supplied to the two cylinders, prove that the following relation is true | ||

C
_{p} - C_{v} = R | ||

where | C_{p} | is the molar heat capacity at constant pressure |

C_{v} | is the molar heat capacity at constant volume | |

R | is the universal gas constant |

**Question 13**

In terms of molecular motion, explain the how evaporation can cause cooling. Give an example of a practical use of the phenomenon of cooling by evaporation. |

**Question 14**

In terms of molecular motion, explain why compressing a gas causes its temperature to increase. Give an example of a practical use of the increase in temperature caused by compressing a gas. |

**Question 15**

Two experiments were done attempting to verify the Boyle/Marriotte law. The graphs below were obtained. In each case the broken line indicates (approximately) the expected result. |

Unfortunately, neither of these graphs verifies the law.
What is the most probable reason for the failure of each experiment? |

**Question 16**

A cylinder has a volume, V, and contains 2.00×10^{-2}mols of oxygen (behaving as an ideal gas) at 20°C and 1.00×10^{5}Pa. The gas is compressed rapidly into a volume V/25. The pressure of the gas increases to 9.06×10^{6}Pa |

a)
| The volume of the has gas been made 25 times smaller. Why has the pressure increased bymore than 25 times? |

b) | Calculate the temperature of the compressed gas assuming that no thermal energy entered of left the gas during the compression. |

c) | Calculate the volume of the cylinder (V). |

d) | If the internal energy of 1mol of oxygen is increased by 12.5J, then the temperature of the gas will increase by 1K. Use this fact to calculate the work done during the compression. |

**Question 17**

A heat engine is used to lift a mass of 200kg. The mass moves 10m vertically upwards. The temperature of the source of the heat engine is 1000K and the "heat sink" is the atmosphere at 293K. Ignoring friction in the engine, pulleys etc, calculate the minimum quantity of thermal energy needed to lift the mass. |