The value of `C_(P) - C_(v) = 1.00 R` for a gas in state `A` and `C_(P) - C_(v) = 1.06 R` in another state. If `P_(A)` and `P_(B)` denote the pressure and `T_(A)` and `T_(B)` denote the temperature in the two states, then

Options

A. `P_(A) = P_(B), T_(A) gt T_(B)`
B. `P_(A) lt P_(B), T_(A) = T_(B)`
C. `P_(A) lt P_(B), T_(A) gt T_(B)`
D. `P_(A) = P_(B), T_(A) lt T_(B)`

Answer

C

Explanation

c. For state `A, C_(P) - C_(v) = R`, i.e., the gas behaves as an ideal gas
For state `B, C_(P) - C_(V) = 1.06 R (!= R)`, i.e., the gas does not behave like an ideal gas.
We know that at high temperature and at low pressure, nature of gas may be ideal.
So we can say that `P_(A) lt P_(B)` and `T_(A) gt T_(B)`,