Question

几个物理问题！

1.You place 3.3 g of water at room temperature in a pressure cooker (a sealed pot) of volume 2.3 L and heat the water to 197 C. What is the pressure in the cooker?
将3.3g的室温水放进2.3L的高压锅里，然后加热至197摄氏度。高压锅内气压是多少？
2.You place 82 moles of hydrogen gas in a balloon of volume 2.4 m3, and find the pressure to be 1.5 times atmospheric pressure. What is the typical speed of a hydrogen molecule?
将82摩尔的氢气放进一个2.4立方米的气球内，且气压为大气压的1.5倍，氢气分子的移动速度是多少？
3.A tank of compressed oxygen gas at a doctor's office has a pressure of 96 times atmospheric pressure. If the volume of the tank is 535 cm3, how many oxygen molecules does it contain?
一个装氧气的容器被放在一声的办公室里，气压是大气压的96倍。如果这个容器的体积是535立方厘米，那么这个容器里有多少氧气分子？

Answer 1

1. Assume the water vapor is an ideal gas.
PV = nRT
P = nRT/V = (3.3/18)*0.082*(197 + 273)/2.3 = 3.07 atmosphere
Here:
n is the number of moles of 3.3g water
R is the gas constant. It's 0.082 when you use atmosphere and liter as the units for pressure and volume respectively
T is the absolute temperature (273 + the number in Celsius)

2. Assume hydrogen is an ideal gas.
V = 2.4 cubic meters = 2400 liters
PV = nRT
T = PV/(nR) = 1.5*2400/(82*0.082) = 535 K
It's not said what type of speed of a hydrogen molecule, so the most probable speed (vp) is used.
vp = √(2RT/M) = √[2*8.31*535/2*10^(-3)] = 2110 m/s
Here R is also gas constant, but 8.31 is used (the value in SI system when pressure in pascal, volume in cubic meters).
The "2*10^(-3)" is the molecular mass of hydrogen, in kg/mol (SI)

(3) Again have to assume oxygen is an ideal gas (probably not a good idea under this kind of pressure).
P = 96 atm
V = 535 cubic cm = 0.535 L
T = 25 + 273 = 298 K (assuming at room temperature of 25°C)
PV = nRT
n = PV/(RT) = 96*0.535/(0.082*298) = 2.10 mol
N = nN0 = 2.10*.6.022*10^23 (N0 is Avogadro number: 6.022*10^23)
= 1.27*10^24
It contains 1.27*10^24 oxygen molecules.

Answer 2

1.思路，水在197摄氏度变成了水蒸气，所以pV/T=NRT,其中P为所求量，V为高压锅的体积2.3L，T为197+273，N为3.3g水的摩尔数。可求P。
2.思路：可以根据麦克斯韦速率分布律来求氢气分子的平均速度或方均根速率。
3.思路，PV/T=NRT,温度取常温

Answer 3

高手