Question
$$600\,c.c$$ of a gas at a pressure of $$750\,mm$$ of $$Hg$$ is compressed to $$500\,c.c.$$ Taking the temperature to remain constant, the increase in pressure, is
A.
$$150\,mm\,\,{\text{of}}\,Hg$$
B.
$$250\,mm\,\,{\text{of}}\,Hg$$
C.
$$350\,mm\,\,{\text{of}}\,Hg$$
D.
$$450\,mm\,\,{\text{of}}\,Hg$$
Answer :
$$150\,mm\,\,{\text{of}}\,Hg$$
Solution :
Given initial volume $$\left( {{V_1}} \right) = 600\,c.c.;$$ Initial
pressure $$\left( {{P_1}} \right) = 750\,mm$$ of $$Hg$$ and final volume $$\left( {{V_2}} \right) = 500\,c.c.$$ according to Boyle’s law,
$$\eqalign{
& {P_1}{V_1} = {P_2}{V_2} \cr
& {\text{or}}\,\,750 \times 600 = {P_2} \times 500 \cr
& {\text{or}}\,\,{P_2} = \frac{{750 \times 600}}{{500}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 900\,mm\,{\text{of}}\,{\text{Hg}} \cr
& {\text{Therefore increase of pressure}} \cr
& {\text{ = }}\left( {900 - 750} \right) \cr
& = 150\,mm\,{\text{of}}\,{\text{Hg}} \cr} $$