I’m just here for points because I have test and I need them lol
Answer:
![T_C = 27+273.15 = 300.15 K](https://tex.z-dn.net/?f=%20T_C%20%3D%2027%2B273.15%20%3D%20300.15%20K)
![T_H = 477+273.15 = 750.15 K](https://tex.z-dn.net/?f=%20T_H%20%3D%20477%2B273.15%20%3D%20750.15%20K)
And replacing in the Carnot efficiency we got:
![e= 1- \frac{300.15}{750.15}= 0.59988 = 59.98 \%](https://tex.z-dn.net/?f=%20e%3D%201-%20%5Cfrac%7B300.15%7D%7B750.15%7D%3D%200.59988%20%3D%2059.98%20%5C%25)
![W_{max}= e* Q_H = 0.59988 * 65000 \frac{KJ}{min}= 38992.2 \frac{KJ}{min}](https://tex.z-dn.net/?f=%20W_%7Bmax%7D%3D%20e%2A%20Q_H%20%3D%200.59988%20%2A%2065000%20%5Cfrac%7BKJ%7D%7Bmin%7D%3D%2038992.2%20%5Cfrac%7BKJ%7D%7Bmin%7D)
Explanation:
For this case we can use the fact that the maximum thermal efficiency for a heat engine between two temperatures are given by the Carnot efficiency:
![e = 1 -frac{T_C}{T_H}](https://tex.z-dn.net/?f=%20e%20%3D%201%20-frac%7BT_C%7D%7BT_H%7D)
We have on this case after convert the temperatures in kelvin this:
![T_C = 27+273.15 = 300.15 K](https://tex.z-dn.net/?f=%20T_C%20%3D%2027%2B273.15%20%3D%20300.15%20K)
![T_H = 477+273.15 = 750.15 K](https://tex.z-dn.net/?f=%20T_H%20%3D%20477%2B273.15%20%3D%20750.15%20K)
And replacing in the Carnot efficiency we got:
![e= 1- \frac{300.15}{750.15}= 0.59988 = 59.98 \%](https://tex.z-dn.net/?f=%20e%3D%201-%20%5Cfrac%7B300.15%7D%7B750.15%7D%3D%200.59988%20%3D%2059.98%20%5C%25)
And the maximum power output on this case would be defined as:
![W_{max}= e* Q_H = 0.59988 * 65000 \frac{KJ}{min}= 38992.2 \frac{KJ}{min}](https://tex.z-dn.net/?f=%20W_%7Bmax%7D%3D%20e%2A%20Q_H%20%3D%200.59988%20%2A%2065000%20%5Cfrac%7BKJ%7D%7Bmin%7D%3D%2038992.2%20%5Cfrac%7BKJ%7D%7Bmin%7D)
Where
represent the heat associated to the deposit with higher temperature.
Answer:
Explanation:
Fist you need to identify where the leak is coming from. You can do this by either listening for the leak or spraying soapy water on the exhaust to look for air bubbles coming out of the exhaust. Depending on the spot of the leak there are many ways you can fix this leak.
1. Exhaust clamp
2. Exhaust putty
3. Exhaust tape
4. New exhaust
Exhaust clamp is best used for holes on straight pipes.
Putty is best used on welds or small holes like on exhaust manifolds or welds connecting various pieces like catalytic converters, mufflers, or resonators.
Tape will work best on straight pipes with holes.
New exhaust is for when the thig is beyond repair, like rust.
Now good luck because working on exhausts is a pain.
Answer:
![0.845\ \text{N}](https://tex.z-dn.net/?f=0.845%5C%20%5Ctext%7BN%7D)
Explanation:
g = Acceleration due to gravity at sea level = ![9.81\ \text{m/s}^2](https://tex.z-dn.net/?f=9.81%5C%20%5Ctext%7Bm%2Fs%7D%5E2)
R = Radius of Earth = 6371000 m
h = Altitude of observatory = 4205 m
Change in acceleration due to gravity due to change in altitude is given by
![g_h=g(1+\dfrac{h}{R})^{-2}\\\Rightarrow g_h=9.81\times(1+\dfrac{4205}{6371000})^{-2}\\\Rightarrow g_h=9.797\ \text{m/s}^2](https://tex.z-dn.net/?f=g_h%3Dg%281%2B%5Cdfrac%7Bh%7D%7BR%7D%29%5E%7B-2%7D%5C%5C%5CRightarrow%20g_h%3D9.81%5Ctimes%281%2B%5Cdfrac%7B4205%7D%7B6371000%7D%29%5E%7B-2%7D%5C%5C%5CRightarrow%20g_h%3D9.797%5C%20%5Ctext%7Bm%2Fs%7D%5E2)
Weight at sea level
![W=mg\\\Rightarrow W=65\times 9.81\\\Rightarrow W=637.65\ \text{N}](https://tex.z-dn.net/?f=W%3Dmg%5C%5C%5CRightarrow%20W%3D65%5Ctimes%209.81%5C%5C%5CRightarrow%20W%3D637.65%5C%20%5Ctext%7BN%7D)
Weight at the given height
![W_h=mg_h\\\Rightarrow W_h=65\times 9.797\\\Rightarrow W_h=636.805\ \text{N}](https://tex.z-dn.net/?f=W_h%3Dmg_h%5C%5C%5CRightarrow%20W_h%3D65%5Ctimes%209.797%5C%5C%5CRightarrow%20W_h%3D636.805%5C%20%5Ctext%7BN%7D)
Change in weight ![W_h-W=636.805-637.65=-0.845\ \text{N}](https://tex.z-dn.net/?f=W_h-W%3D636.805-637.65%3D-0.845%5C%20%5Ctext%7BN%7D)
Her weight reduces by
.
Answer:
a) 149 kJ/mol, b) 6.11*10^-11 m^2/s ,c) 2.76*10^-16 m^2/s
Explanation:
Diffusion is governed by Arrhenius equation
![D = D_0e^{\frac{-Q_d}{RT} }](https://tex.z-dn.net/?f=D%20%3D%20D_0e%5E%7B%5Cfrac%7B-Q_d%7D%7BRT%7D%20%7D)
I will be using R in the equation instead of k_b as the problem asks for molar activation energy
I will be using
![R = 8.314\ J/mol*K](https://tex.z-dn.net/?f=R%20%3D%208.314%5C%20J%2Fmol%2AK)
and
°C + 273 = K
here, adjust your precision as neccessary
Since we got 2 difusion coefficients at 2 temperatures alredy, we can simply turn these into 2 linear equations to solve for a) and b) simply by taking logarithm
So:
![ln(6.69*10^{-17})=ln(D_0) -\frac{Q_d}{R*(1030+273)}](https://tex.z-dn.net/?f=ln%286.69%2A10%5E%7B-17%7D%29%3Dln%28D_0%29%20-%5Cfrac%7BQ_d%7D%7BR%2A%281030%2B273%29%7D)
and
![ln(6.56*10^{-16}) = ln(D_0) -\frac{Q_d}{R*(1290+273)}](https://tex.z-dn.net/?f=ln%286.56%2A10%5E%7B-16%7D%29%20%3D%20ln%28D_0%29%20-%5Cfrac%7BQ_d%7D%7BR%2A%281290%2B273%29%7D)
You might notice that these equations have the form of
![d=y-ax](https://tex.z-dn.net/?f=d%3Dy-ax)
You can solve this equation system easily using calculator, and you will eventually get
![D_0 =6.11*10^{-11}\ m^2/s\\ Q_d=1.49 *10^3\ J/mol](https://tex.z-dn.net/?f=D_0%20%3D6.11%2A10%5E%7B-11%7D%5C%20m%5E2%2Fs%5C%5C%20Q_d%3D1.49%20%2A10%5E3%5C%20J%2Fmol)
After you got those 2 parameters, the rest is easy, you can just plug them all including the given temperature of 1180°C into the Arrhenius equation
![6.11*10^{-11}e^{\frac{149\ 000}{8.143*(1180+273)}](https://tex.z-dn.net/?f=6.11%2A10%5E%7B-11%7De%5E%7B%5Cfrac%7B149%5C%20000%7D%7B8.143%2A%281180%2B273%29%7D)
And you should get D = 2.76*10^-16 m^/s as an answer for c)