Question

One mole of an ideal gas is at temperature \( T \) K. The \( \gamma \) value of this gas is \( \frac{5}{3} \). Now the gas does 12R Joules of work adiabatically (R is the universal gas constant). Then the final temperature of the gas will be:

• A. \( T - 8 \, \text{K} \)
• B. \( T + 4 \, \text{K} \)
• C. \( T - 4.4 \, \text{K} \)
• D. \( T - 6 \, \text{K} \)

Hint:

In adiabatic processes, the relationship between temperature and work done is crucial to finding the final temperature.

Answer 1

The Correct Option is A

For an adiabatic process, the relation between temperature and work done is given by: \[ W = \frac{P_{\text{final}} V_{\text{final}} - P_{\text{initial}} V_{\text{initial}}}{1 - \gamma} \] For a monoatomic ideal gas with \( \gamma = \frac{5}{3} \), the final temperature \( T_f \) is given by: \[ T_f = T_i - \frac{8R}{m} \] Thus, the final temperature will be \( T - 8 \, \text{K} \).