A block of copper at a pressure of 1 atm, a volume of 100 cm3, and a temperature of 10°C experiences a rise in temperature of 5°C and an increase in volume of 0.005 cm3. Assuming the volume expansivity and isothermal compressibility given in given Problem, calculate the final pressure.
Problem
(a) A block of copper at a pressure of 1 atm (approximately 100 kPa) and a temperature of 5°C is kept at constant volume. If the temperature is raised to 10°C, what will be the final pressure?
(b) If the vessel holding the block of copper has a negligibly small thermal expansivity and can withstand a maximum pressure of 1000 atm, what is the highest temperature to which the system may be raised? (Note: The volume expansivity ß and isothermal compressibility K, are not always listed in handbooks of data.
However, ß is three times the linear expansion coefficient Q, and K, is the reciprocal of the bulk modulus B. For this problem, assume that the volume expansivity and isothermal compressibility remain practically constant within the temperature range of 0 to 20°C at the values of 4.95 x 10-5 K-1 and 6.17 x 10-12 Pa-1, respectively.)