Question

A monoatomic gas at 27°C is adiabatically compressed to 80% of its initial volume. Find the final temperature of the gas.

Answer 1

Given: V_f = 0.8 V_i ; T_i = 27 + 273 = 300 K,

To find: T_f = ?

y = `5/3 `      ...(mono-atomic)

∴ (T_iV_i)^y-1 = (T_fV_f) ^y-1

∴ `T_f = T_i (V_i/V_f) ^(y-1)`

= `300(1.25)^(5/3-1)`     ...(∵ V_f = 0.8V_i)

= `300(1.25)^(2/3)`

= (300) (1.161)

= 348.3 K = (348.3 - 273)°C

 ∴ T_f = 75.3°C is the final temperature of the gas