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For a given gas, T(C) = 40 K, then T(i) ...

For a given gas, `T_(C) = 40 K`, then `T_(i)` is

A

40 K

B

270 K

C

135 K

D

540 K

Text Solution

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The correct Answer is:
To find the inversion temperature \( T_i \) for a gas given that the critical temperature \( T_c \) is 40 K, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Relationship**: The inversion temperature \( T_i \) is related to the critical temperature \( T_c \) by the formula: \[ T_c = \frac{4}{27} T_i \] 2. **Substitute the Given Value**: We know that \( T_c = 40 \, \text{K} \). Substitute this value into the equation: \[ 40 = \frac{4}{27} T_i \] 3. **Rearrange the Equation**: To isolate \( T_i \), multiply both sides of the equation by \( \frac{27}{4} \): \[ T_i = 40 \times \frac{27}{4} \] 4. **Calculate \( T_i \)**: Now perform the multiplication: \[ T_i = 40 \times \frac{27}{4} = 40 \times 6.75 = 270 \, \text{K} \] 5. **Final Result**: Therefore, the inversion temperature \( T_i \) is: \[ T_i = 270 \, \text{K} \] ### Summary: The inversion temperature \( T_i \) for the gas is 270 K.
To find the inversion temperature \( T_i \) for a gas given that the critical temperature \( T_c \) is 40 K, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Relationship**: The inversion temperature \( T_i \) is related to the critical temperature \( T_c \) by the formula: \[ T_c = \frac{4}{27} T_i ...
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