Answer to Question #142409 in Optics for Muhammad Kamran

Question

An ideal gas at temperature 300 K is contained under the weightless piston in a vertical cylinder. The piston area is 200 cm^2 and the atmospheric pressure is 10^5 Pa. The gas in the cylinder is heated and the piston is loaded with a weight of mass 10 kg. Find the change in gas temperature if the piston position has not changed. The answer should be expressed in kelvin [K]. Let the free fall acceleration be 10 m/s^2.

Answer 1

Answer

T₁=300K

P₁=10⁵pa

So P₂ can be calculated as

P₂=F/A+P_atm

F/A=$\frac{mg}{A}=\frac{100}{0.02}=5000Pa$

$P_2=0.05\times10^5+10^5=1.05\times10^5Pa$

Volume is constant so

$\frac{P}{T}=constant$

$\frac{P_1}{T_1}=\frac{P_2}{T_2}$

$\frac{10^5}{300}=\frac{1.05\times10^5}{T_2}$

$T_2=315K$