(2) Calculate thermal expansion coefficient a = (7) and isothermal compressibility k = р - (3) for the following gases: T (a) Ideal gas (1 mol), pV = RT (b) Van der Waals gas (1 mol), (p + 2) (V − b) = RT (c) Non-ideal gas (1 mol), pV = RT (1 − B(T)) (B is called second virial coefficient)
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- Consider a gas that follows the equation of state NRT aN² 2 P V - bN V2 This is called van der Waals gas (a,b > 0). For temperatures T > Tc : monotonically decreasing function. Assume T > Tc and Cy = 3NR/2. = 8a p(V) is a 27Rb Consider an insulated box with volume V₁. The box was divided by a wall. One of the compartments had volume Vo at temperature To, which was filled with van der Waals gas of amount N. The other compartment was vacuum. The system was in equilibrium. (i) The wall was removed abruptly. The gas expanded and occupied the entire box. This process is called adiabatic free expansion. The temperature in the box is now T₁ in equilibrium. What is T₁ - To? (ii) The internal energy of the gas does not change by adiabatic free expansion. Why? (iii) Instead of the abrupt removal, the wall was moved through adiabatic and quasi-static process, and the gas expanded to the entire volume of the box. The temperature in the box is now T2 in equilibrium. What is T₂? (iv) Show T₁ > T₂,…The molar specific heat at constant pressure of an ideal gas is (7/2)R. The ratio of specific heat at constant pressure to that at constant volume is (a) 7/5 (b) 8/7 (c) 5/7 (d) 9/7If one mole of a monoatomic gas of (y = 5/3) is mixed with one mole of diatomic gas, then the (y = 715) value of y for the mixture will be, (a) 1.5 (b) 1.54 (c) 1.4 (d) 1.45
- You need to design a gas with a y (= Cp/Cv) value of 1.5. While no individual gas has this value, you could produce such a gas by mixing together a monatomic gas and a diatomic gas. What fraction or percentage of the molecules in the mixture needs to be monatomic? [Hint: for a monatomic gas Cv = (3/2)R and for a diamotic gas Cy (5/2) R.] =A shipment from Earth to Mars contains a 50 gallon [gal] tank filled with an ideal gas. The molecular weight of the ideal gas is 15.9 grams per mole [g/mol]. NASA tells the astronauts on Mars that the tank and gas combined had an initial total mass of 5 kilograms [kg] and the pressure was 3 atmospheres [atm] before it left the Earth. During the trip, the temperature was kept constant at 20 degrees Celsius [°C]. When it arrives on Mars, the astronauts check the sensors and discover the pressure is 2.2 atmospheres [atm] and the temperature is 20 degrees Celsius [°C]. Based on this information, the astronauts determine that some of the gas leaked during shipment. Determine how much gas leaked from the tank in units of grams [g]. Gravity on Mars = 3.71 meters per second squared[m/s2].(a) How many molecules are present in a sample of an ideal gas that occupies a volume of 1.90 cm3, is at a temperature of 20°C, and is at atmospheric pressure? molecules (b) How many molecules of the gas are present if the volume and temperature are the same as in part (a), but the pressure is now 1.80 ✕ 10−11 Pa (an extremely good vacuum)? molecules
- A 1.70-mol sample of hydrogen gas is heated at constant pressure from 302 K to 426 K. (a) Calculate the energy transferred to the gas by heat. kJ (b) Calculate the increase in its internal energy. k] (c) Calculate the work done on the gas. kJ(a) A rigid tank contains 1.50 moles of carbon dioxide, which can be treated as an ideal gas, at a pressure of 22.7 atm. While the tank and gas maintain a constant volume and temperature, a number of moles are removed from the tank, reducing the pressure to 5.10 atm. How many moles are removed? mol (b) What If? In a separate experiment beginning from the same initial conditions, including a temperature T, of 25.0°C, half the number of moles found in part (a) are withdrawn while the temperature is allowed to vary and the pressure undergoes the same change from 22.7 atm to 5.10 atm. What is the final temperature (in °C) of the gas? °CA sample consists of an amount n in moles of a monatomic ideal gas. The gas expands adiabatically, with work W done on it. (Work W is a negative number.) The initial temperature and pressure of the gas are Ti and Pi. Calculate (a) the final temperature and (b) the final pressure.