Thermal Physics Questions

Thermal Physics 1. Estimate the number of molecules in a flask of volume 5.0 × 10-4 m3 containing oxygen at a pressure of 2.0 × 105 Pa and a temperature of 300 K. [2.4 × 1022] 2. At the triple point of water the pressure of a fixed mass of gas is 2680 Pa. The temperature is changed to T while the volume of the gas is kept constant. The pressure is then 4870 Pa. (i) Find the value of T [496 K] (ii) What is the advantage of making this determination at such a low pressure? 3. Taking the molar gas constant to be 8.31 JK-1mol-1, estimate the molar volume of a gas at 300 K and at a pressure of 1.000 × 105 Pa. [0.025 m3 mol-1] The volume of a single molecule is estimated to be 2.000 × 10`-29 m3. What fraction of the volume occupied by the gas is empty? [0.9995] 4, Two equal glass bulbs A and B are joined by a narrow capillary tube of negligible volume. B can be connected to the atmosphere through a tap. Initially this tap is open and B is kept at room temperature at 20˚, while A is warmed to 100˚C. The tap is then shut and bulb A is allowed to cool to 20˚. Find the final pressure in the bulbs. [9.0× 104Pa] 5 Derive from the definitions of density and pressure, the equation p=ρgh for the pressure exerted by a column of liquid height h and density ρ. (b)(i) using the kinetic model of the gas, explain how a pressure is exerted by a gas (ii) Calculate the root-mean-square speed of gas molecules in a gas at pressure 1.05× 105 Pa and density 1.29 kgm-3 (not in syllabus) (c)(i) An ideal gas is defined as one for which, at constant pressure, the volume of the gas is proportional to the absolute temperature. Calculate the absolute temperature T when an ideal gas has volume 0.00783 m3, assuming that the same mass of the ideal gas had volume 0.0308 m3 when at the same pressure and at temperature 273 K. (ii) Express 273 K and your value of T from (iii) as temperatures measured on the Celsius scale. 6. A container of gas holds 3.6 × 1025 molecules of an ideal gas each with a mass of 4.6 × 10-26 kg. The root-mean-square speed of the molecules is 270 ms-1 and the container is on an aircraft travelling at 240 ms-1. Calculate (i) the knetic energy as a result of the random motion of all the molecules in the gas (ii) the kinetic energy the gas has as a result of being on the aircraft (iii) the internal energy of the gas 7. The behaviour of a fixed mass of gas which is assumed to be ideal is as follows: The gas starts at A with a volume of 5.00× 10-4 m3, a temperature of 300 K and a pressure of 1.00 × 105 Pa. In the change A to B it is compressed to a volume of 7.00 × 10-5 m3; the pressure rises to 1.50 × 106 Pa and the temperature to 630 K.

(a) Use the equation of state for an ideal gas to find the number of moles in the fixed mass of gas (b) In the change from B to C, the temperature of the gas rises from 630 K to 1500 K. The molar heat capacity at constant volume of the gas is 21 JK-1mol-1. Calculate the thermal energy supplied in this change. (c) How much work is done by the gas in the change B to C ? (d) In the change from C to D , the gas expands to its original volume. The temperature at D is 680 K. Calculate the pressure at D (e) Sketch the P-V graph for this ideal gas, indicating the states at A, B, C and D