134 lines
4.9 KiB
Python
134 lines
4.9 KiB
Python
#!/usr/bin/env python3
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# -*- coding: utf-8 -*-
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"""
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绘制黑体辐射曲线
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本脚本绘制温度为25000K和35000K的理论黑体辐射曲线
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"""
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import numpy as np
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import matplotlib.pyplot as plt
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from scipy import constants as const
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import matplotlib.font_manager as fm
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from matplotlib.ticker import ScalarFormatter
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# 检查是否有中文字体
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try:
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chinese_font = fm.FontProperties(fname='/usr/share/fonts/truetype/droid/DroidSansFallbackFull.ttf')
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except:
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# 如果找不到指定中文字体，尝试使用系统默认字体
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chinese_font = fm.FontProperties()
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# 物理常数
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h = const.h # 普朗克常数，J·s
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c = const.c # 光速，m/s
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k = const.k # 玻尔兹曼常数，J/K
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# 普朗克函数计算黑体辐射
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def planck(wavelength, T):
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"""
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计算黑体辐射的辐射强度
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参数:
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wavelength: 波长，单位：米
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T: 温度，单位：开尔文
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返回:
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B_lambda: 黑体辐射强度，单位：W·m^-2·steradian^-1·m^-1
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"""
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a = 2.0 * h * c**2
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b = h * c / (wavelength * k * T)
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B_lambda = a / (wavelength**5 * (np.exp(b) - 1.0))
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return B_lambda
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# 维恩位移定律：λ_max * T = b，其中b ≈ 2.8978e-3 m·K
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def wien_peak(T):
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"""计算维恩位移定律预测的峰值波长（米）"""
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b = 2.8978e-3 # 维恩常数，m·K
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return b / T
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# 设置温度
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T1 = 25000 # 25000K
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T2 = 35000 # 35000K
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# 计算峰值波长
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peak_wavelength_T1 = wien_peak(T1)
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peak_wavelength_T2 = wien_peak(T2)
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# 转换为纳米
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peak_wavelength_T1_nm = peak_wavelength_T1 * 1e9
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peak_wavelength_T2_nm = peak_wavelength_T2 * 1e9
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# 设置波长范围（纳米）- 调整范围以更好地显示峰值
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wavelength_nm = np.linspace(10, 1000, 1000)
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wavelength_m = wavelength_nm * 1e-9 # 转换为米
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# 计算不同温度的黑体辐射强度
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intensity_T1 = planck(wavelength_m, T1)
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intensity_T2 = planck(wavelength_m, T2)
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# 绘图设置
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plt.figure(figsize=(12, 8))
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# 创建主图和次坐标轴（线性刻度）
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plt.subplot(211) # 第一个子图：线性刻度
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plt.plot(wavelength_nm, intensity_T1, 'r-', linewidth=2, label=f'T = {T1}K')
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plt.plot(wavelength_nm, intensity_T2, 'b-', linewidth=2, label=f'T = {T2}K')
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# 标记维恩峰值
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plt.axvline(x=peak_wavelength_T1_nm, color='r', linestyle='--', alpha=0.7)
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plt.axvline(x=peak_wavelength_T2_nm, color='b', linestyle='--', alpha=0.7)
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plt.annotate(f'峰值：{peak_wavelength_T1_nm:.1f}nm',
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xy=(peak_wavelength_T1_nm, planck(peak_wavelength_T1*1e-9, T1)),
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xytext=(peak_wavelength_T1_nm+50, planck(peak_wavelength_T1*1e-9, T1)*0.8),
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arrowprops=dict(arrowstyle='->'), fontproperties=chinese_font)
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plt.annotate(f'峰值：{peak_wavelength_T2_nm:.1f}nm',
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xy=(peak_wavelength_T2_nm, planck(peak_wavelength_T2*1e-9, T2)),
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xytext=(peak_wavelength_T2_nm+50, planck(peak_wavelength_T2*1e-9, T2)*0.8),
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arrowprops=dict(arrowstyle='->'), fontproperties=chinese_font)
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plt.xlabel('波长 (nm)', fontproperties=chinese_font)
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plt.ylabel('辐射强度 (W·m⁻²·sr⁻¹·m⁻¹)', fontproperties=chinese_font)
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plt.title('黑体辐射曲线 - 线性刻度', fontproperties=chinese_font)
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plt.legend(prop=chinese_font)
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plt.grid(True, alpha=0.3)
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plt.xlim(0, 500) # 限制X轴范围以更好地显示峰值
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# 第二个子图：对数刻度
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plt.subplot(212)
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plt.loglog(wavelength_nm, intensity_T1, 'r-', linewidth=2, label=f'T = {T1}K')
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plt.loglog(wavelength_nm, intensity_T2, 'b-', linewidth=2, label=f'T = {T2}K')
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# 标记维恩峰值（对数刻度）
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plt.axvline(x=peak_wavelength_T1_nm, color='r', linestyle='--', alpha=0.7)
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plt.axvline(x=peak_wavelength_T2_nm, color='b', linestyle='--', alpha=0.7)
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plt.annotate(f'峰值：{peak_wavelength_T1_nm:.1f}nm',
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xy=(peak_wavelength_T1_nm, planck(peak_wavelength_T1*1e-9, T1)),
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xytext=(peak_wavelength_T1_nm*2, planck(peak_wavelength_T1*1e-9, T1)/5),
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arrowprops=dict(arrowstyle='->'), fontproperties=chinese_font)
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plt.annotate(f'峰值：{peak_wavelength_T2_nm:.1f}nm',
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xy=(peak_wavelength_T2_nm, planck(peak_wavelength_T2*1e-9, T2)),
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xytext=(peak_wavelength_T2_nm*2, planck(peak_wavelength_T2*1e-9, T2)/5),
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arrowprops=dict(arrowstyle='->'), fontproperties=chinese_font)
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plt.xlabel('波长 (nm)', fontproperties=chinese_font)
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plt.ylabel('辐射强度 (W·m⁻²·sr⁻¹·m⁻¹)', fontproperties=chinese_font)
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plt.title('黑体辐射曲线 - 对数刻度', fontproperties=chinese_font)
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plt.legend(prop=chinese_font)
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plt.grid(True, alpha=0.3, which='both')
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# 添加总标题
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plt.suptitle(f'温度为{T1}K和{T2}K的黑体辐射曲线对比', fontsize=16, fontproperties=chinese_font)
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# 显示图形
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plt.tight_layout()
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plt.subplots_adjust(top=0.9) # 为总标题留出空间
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plt.show()
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# 打印维恩峰值信息
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print(f"维恩位移定律预测的峰值波长:")
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print(f"T = {T1}K: {peak_wavelength_T1_nm:.2f}纳米")
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print(f"T = {T2}K: {peak_wavelength_T2_nm:.2f}纳米") |