## Adding a temperature dependency

### Paper reference: Yu et al (2017)
Yu, F., Luo, G., Nadykto, A. B., & Herb, J. (2017). Impact of temperature dependence on the possible contribution of organics to new particle formation in the atmosphere. Atmospheric Chemistry and Physics, 17(8), 4997–5005. https://doi.org/10.5194/acp-17-4997-2017


\begin{equation}
f_T = exp \Big[ \frac{\Delta H}{k} \big( \frac{1}{T} - \frac{1}{T_0} \big) \Big]
\end{equation}

- Best fit with obsevations according to Yu et al (2017) is by $\Delta H = 35$ kcal/mol.
- $T_0 = 278.$ 
- $k= 1.380649 \times 10^{−23}$ J/K
- $k = 0.001985875$ kcal/mol/K


It is unclear how the authors set the maximum value, but they say in the review that they initially used 10 as a max and that the difference was negligible. 


```python
import numpy as np
```


```python
T_0 = 278
k_kcalmolK =  0.001985875 
dH = 35

def fT(T, max=10):
    f =  np.exp(dH/k*(1/T-1/T_0))
    if type(T) is np.ndarray:
        f[f>10] = 10
    else:
        f = min(f,10)
    return f
```


```python
fT(270)
```




    6.5432960174993715




```python
T = np.linspace(270,310)


f = fT(T)

import matplotlib.pyplot as plt
plt.plot(T,f)
plt.yscale('log')
plt.xlim([270,310])
plt.ylim([1e-3,10])
```


```python
a = [1,2,4]
```


```python
[]
```




    []




```python
type(T)
```




    numpy.ndarray




```python

```

bf0c5eb4cfadb030967084f9d9837fb15d3fd8d2
ipynb
Jupyter Notebook
oas_erf/notebooks/06_review/x_check_yu_2017.ipynb
sarambl/OAS-ERF
7510c21a630748eda2961608166227ad77935a67
MIT
oas_erf/notebooks/06_review/x_check_yu_2017.ipynb
sarambl/OAS-ERF
7510c21a630748eda2961608166227ad77935a67
MIT
oas_erf/notebooks/06_review/x_check_yu_2017.ipynb
sarambl/OAS-ERF
7510c21a630748eda2961608166227ad77935a67
MIT
Qwen/Qwen-72B
1. YES
2. YES