Two moles of an ideal gas with (C_(P))/(C_(V))= (5)/(3) are mixed with 3 moles of another ideal gas with (C_(P))/(C_(V))= (4)/(3). The value of (C_(P))/(C_(V)) for the mixture is

Two moles of an ideal gas with (C_(P))/(C_(V))= (5)/(3) are mixed with

1.	Two moles of an ideal gas with (C_(P))/(C_(V))= (5)/(3) are mixed with 3 moles of another ideal gas with (C_(P))/(C_(V))= (4)/(3). The value of (C_(P))/(C_(V)) for the mixture is
Answer» <P>1.38 1.42 1.5 1.7 Solution :`C_(P)- C_(V)= R` and for first gas `(C_(P_(1)))/(C_(V_(1)))= (5)/(3) rArr C_(P_(1)) = (5)/(3) C_(V_(1))` Now `C_(P_(1))- C_(V_(1))= R` `:. (5)/(3) C_(V_(1))- C_(V_(1))= R` `:. 5C_(V_(1))- 3C_(V_(1)) = 3R` `:. 2C_(V_(1))= 3R` `:. C_(V_(1)) = (3R)/(2)` and `C_(P_(1)) = C_(V_(1)) + R` `=(3R)/(2) + R` `:. C_(P_(1)) = (5R)/(2)` Now for second gas `(C_(P_(2)))/(C_(V_(2))) = (4)/(3)` `:. C_(P_(2)) = (4)/(3) C_(V_(2))` and `C_(P_(2))- C_(V_(2)) R` `:. (4)/(3) C_(V_(2))-C_(V_(2))R` `:. 4C_(V_(2)) -3C_(V_(2)) = 3R` `:. C_(V_(2)) = 3R` and `C_(P_(2)) = C_(V_(2)) + R` `=3R + R` `:. C_(P_(2)) = 4R` `:.` For mixture `(C_(P))/(C_(V)) = (n_(1)C_(P_(1)) + n_(2) C_(P_(2)))/(n_(1) C_(V_(1)) + n_(2) C_(V_(2)))` `n_(1)=2` mole, `n_(2)=3` mole `:. (C_(P))/(C_(V)) = (2 xx (5R)/(2) + 3 xx 4R)/(2 xx (3R)/(2) + 3 xx 3R)` `=(5R + 12R)/(3R + 9R) = (17R)/(12R)` `=(17)/(12)= 1.4166` `=1.42`