Understanding Thermal Voltage Calculation
The question asks us to find the thermal voltage at a specific temperature. The thermal voltage ($V_T$) is a concept often used in semiconductor physics and electronics. It represents the voltage equivalent of thermal energy ($kT$) per charge carrier ($q$).
Key Formula for Thermal Voltage
The formula to calculate thermal voltage is:
$ V_T = \frac{k_B T}{q} $Where:
- $V_T$ is the thermal voltage.
- $k_B$ is the Boltzmann's constant, given as $1.38 \times 10^{-23}$ J/K.
- $T$ is the absolute temperature in Kelvin (K).
- $q$ is the elementary charge, which is approximately $1.602 \times 10^{-19}$ Coulombs (C).
Step 1: Convert Temperature to Kelvin
The temperature is given in Celsius (°C), but the formula requires the temperature in Kelvin (K). The conversion formula is:
$ T(\text{K}) = T(\text{°C}) + 273.15 $Given the temperature is 47°C:
$ T = 47 + 273.15 = 320.15 \text{ K} $Step 2: Calculate Thermal Voltage
Now, substitute the values into the thermal voltage formula:
$ V_T = \frac{(1.38 \times 10^{-23} \text{ J/K}) \times (320.15 \text{ K})}{1.602 \times 10^{-19} \text{ C}} $First, calculate the numerator:
$ k_B T = (1.38 \times 10^{-23}) \times 320.15 \approx 4.41807 \times 10^{-21} \text{ J} $Now, divide by the elementary charge ($q$):
$ V_T = \frac{4.41807 \times 10^{-21} \text{ J}}{1.602 \times 10^{-19} \text{ C}} $Performing the division:
$ V_T \approx 0.02758 \text{ V} $Step 3: Convert Result to Millivolts (mV)
The options are given in millivolts (mV). To convert Volts (V) to millivolts (mV), multiply by 1000:
$ V_T (\text{mV}) = 0.02758 \text{ V} \times 1000 \text{ mV/V} $ $ V_T \approx 27.58 \text{ mV} $Rounding the result to one decimal place gives 27.6 mV.
Step 4: Compare with Options
Let's compare our calculated result with the given options:
- Option 1: 27.6 mV
- Option 2: 27.6 V
- Option 3: 27.6 $ \mu V $
- Option 4: 2.76 V
Our calculated value of approximately 27.6 mV matches Option 1.
Important Questions from Miscellaneous
- Which of the following relationships is/are not true?
(A). Most probable velocity = $\sqrt{\frac{2RT}{M}}$
(B). PV = $\frac{3}{2}kT$
(C). Compressibility factor Z = $\frac{pV}{nRT}$
(D). Average kinetic energy of gas = $\frac{1}{2}kT$
Choose the correct answer from the options given below - Match List-I with List-II
List-I List-II Electronic Configuration First Ionisation energy (kJ mol$^{-1}$) (A). ns$^2$ (I). 2100 (B). ns$^2$np$^1$ (II). 1400 (C). ns$^2$np$^3$ (III). 800 (D). ns$^2$np$^6$ (IV). 900
Choose the correct answer from the options given below: - The shielding constant of a 2p electron (calculated using Slater's rules) is
- Match List-I with List-II
List-I List-II Spectroscopy Property (A). Raman (I). Polarizability (B). FTIR (II). Dipole Moment (C). UV-Visible (III). Absorbance (D). NMR (IV). Spin
Choose the correct answer from the options given below: - The structure of protein comprises of:
(A). Primary structure of protein is associated with amino acids
(B). Secondary structure of protein is associated to peptides
(C). Tertiary structure of protein is associated with polypeptide chains
(D). Quaternary structure of protein is associated with polypeptide chains
Choose the correct answer from the options given below:
