Problem 2: Helium is a very important element for both industrial and research applications. In its gas form it can be used for welding, and since it has a very low melting point (only 0.95 K under 2.5 MPa) it can be used in liquid form to cool superconducting magnets, such as those found in particle physics experiments. Say we have a cylinder of n = 145 moles of Helium gas at room temperature (T = 20° C). The cylinder has a radius of r = 17.5 cm and a height h = 1.45 m.
Part (a) What pressure (in kPa) is the helium gas under?
P = ______
Part (b) Helium is usually kept in the highest pressure gas cylinders, which can typically withstand at least 500 atm of pressure. Would the tank in part (a) be able to maintain its structural integrity?
Part (c) In principle, these tanks could fail if the temperature of the Helium started rising - if they were stored in a hot environment, for instance. To determine how much of a danger this is, calculate the temperature (in C) the Helium gas would have to be to make the tank start to crack.
Tmax = ______
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- P2 657°C Isothermal 2.0 atm 37°C 3 0+ V(L) V3 The figure (not to scale) shows a pV diagram for 3.4 g of helium gas (He) that undergoes the process 1 → 2 → 3→1. The ideal gas constant is R = 8.314 J/mol · K = 0.0821 L· atm/mol · K, and the atomic weight of helium is 4.0 g/mol. What is the net work done by the gas in Joules? Please give your numerical answer with one decimal place.arrow_forward1. For nitrogen at 285 K find, a) The most probable speed b) The average speed c) The rms speed The molar mass of nitrogen is 14.0 g/mol and R=8.31 kg/(mol K) Hint: You need to convert quantities into Sl units. m/s m/s m/sarrow_forwardFor any gas, C C. - (+7), (7), Suppose you have one mole of a gas that obeys the equation of state, p(v- b) = represents the volume taken up by the molecules in the system, and 3.5 bars and T = 425 K for your gas sample. Hint: Use the equation of state to evaluate the partial derivatives. =RT, where b is the molar volume. Find the value of A if C-C₁=AR when P = 6arrow_forward
- 1. (a) What is the average kinetic energy in joules of a hydrogen atom on the 5500 °C surface of the Sun? The Boltzmann's constant is k=1.38x10-23 J/K J KE av: (b) What is the average kinetic energy of a helium atom in a region of the solar corona where the temperature is 6 x 105⁰K? KE av: Jarrow_forwardAn ideal gas is confined to a container at a temperature of 330 K. 1)What is the average kinetic energy of an atom of the gas? (Express your answer to two significant figures.)arrow_forward1. An expensive vacuum system can achieve a pressure as low as 1 x 10-7N/m² at 20 °C. How many atoms are there in a cubic centimeter at this pressure and temperature? The Boltzman's constant k= 1.38 x 10 m²kg/(s²K) -23 Number of atoms:arrow_forward
- A sealed 73 m tank is filled with 8000 moles of ideal oxygen gas (diatomic) at an initial temperature of 270 K. The gas is heated to a final temperature of 390 K. The atomic mass of oxygen is 16.0 g/mol. The mass density of the oxygen gas, in Sl units, is closest to: O 7.0 O 4.4 O 2.6 О 35 O 1.8arrow_forward1. (a) What is the average kinetic energy in joules of a hydrogen atom on the 5500 °C surface of the Sun? The Boltzmann's constant is k=1.38×10-23 J/K J KE av (b) What is the average kinetic energy of a helium atom in a region of the solar corona where the temperature is 6 x 105⁰K? KE Fav Jarrow_forward6. The following data show the relation of vapour pressure of liquid Z as a function of temperature. p/mmHg T/°C 17.54 20 31.82 30 55.32 40 92.51 50 149.38 60 233.70 70 Using linear regression technique, compute the molar enthalpy of vaporization of liquid Z!arrow_forward
- For this question there could be one or MULTIPLE answers, Choose the best Match/Matches. For a monatomic ideal gas in thermal equilibrium near room temperature, a. U = 3/2 NkT. b. U = 5/2 NkT. c. degrees of freedom include translational and rotational motions. d. degrees of freedom include translational, rotational, and vibrational motions. e. U = 5/2 pV. f. U = 3/2 pV. Explain work please.arrow_forward2. For T = 300 K, calculate the pressure (in bars) at which the mean free path of a hydrogen molecule will be each of the lengths given here. For H₂, o = 2.30 x 10-1⁹ m². (a) 100 μm (b) 1.00 mm (c) 1.00 m LLarrow_forward* ? 63. During isothermal compression, the internal energy of an ideal gas : a. Decreases b. Can go either way depending on the precise pressures and volumes c. Stays the same d. Increases 64. What is the total internal energy of a sample of 9 moles of air (considered as an ideal gas) at a temperature of 3°C? Assume that the rotational degrees of freedom are fully activated, and that the vibrational modes are "frozen out". (k=1.38 x 10-23 J/K, N-6.022x10²3) 3°C = 273+3 = 276 U= n NAF ( 1₂ KT) (9)(6.022 X 10²²) x 1.38×10²³ x 276) = 1032 a. 1.19 x 105 J b. 9.29 x 104 J c. 7.23 x 104 J d. 5.16 x 104 J 65. What is the average translational kinetic energy per oxygen molecule in this sample? a. 1.2 x 10-20 J b. 9.14 x 10-21 J c. 5.71 x 10-21 J d. 1.54 x 10-20 J 66. Is this kinetic energy the same or different from the nitrogen molecules in the sample? a. Different b. The same 67. What is the rms speed of the oxygen molecules in this sample? (the atomic mass number of oxygen is 15.994, 1 u =…arrow_forward