Question 44: Thermodynamics & KTG

Question

The ratio of specific heat capacities at constant pressure to that at constant volume for a given mass of a gas is $\frac{5}{2}$. If the percentage increase in volume of the gas while undergoing an adiabatic change is $\frac{3}{2}$, then the percentage decrease in pressure will be:

Accepted Answer

We have an adiabatic law
$$P\,V^\gamma = 	ext{constant},\qquad \gamma = \frac{C_p}{C_v} = \frac{5}{2}.$$
If the volume increases by 1.5Ã¢ÂÂ% (i.e.\ ÃÂV/V = +3/2Ã¢ÂÂ%), then for small changes one may linearize:
$$\frac{\Delta P}{P}\approx -\gamma\,\frac{\Delta V}{V} = -\frac{5}{2}	imes\frac{3}{2}\% = -\frac{15}{4}\%.$$
So the pressure falls by 15/4Ã¢ÂÂ%, which is option A.

Answer

$\frac{15}{4}$

Answer

$\frac{3}{5}$

Answer

$\frac{4}{15}$

Answer

$\frac{5}{3}$

Thermodynamics & KTG

The ratio of specific heat capacities at constant pressure to that at constant volume for a given mass of a gas is \frac{5}{2}. If the percentage increase in volume of the gas while undergoing an adiabatic change is \frac{3}{2}, then the percentage decrease in pressure will be:

Choose the correct answer: