A vertical cylinder closed at both ends is fitted with a smooth piston dividing the volume into two parts each containing one mole of air. At the equilibrium temperature of 320 K, the upper and lower parts are in the ratio 4:1. The ratio will become 3:1 at a temperature of

A vertical cylinder closed at both ends is fitted with a smooth piston

1.	A vertical cylinder closed at both ends is fitted with a smooth piston dividing the volume into two parts each containing one mole of air. At the equilibrium temperature of 320 K, the upper and lower parts are in the ratio 4:1. The ratio will become 3:1 at a temperature of
Answer» 450 K 228 K 420 K 570 K Solution :`(p_(2)-p_(1))A=mg` or `""(mg)/A=(RT_(1))/(V_(i))-(RT_(i))/(4V_(1))=(3RT_(i))/(4V_(1))` SIMILARLY in second CASE, `""(mg)/A=(RT_(f))/(V_(2))-(RT_(f))/(3V_(2))=(3RT_(f))/(3V_(2))` Further `5V_(1)=4V_(2)` Equating EQS. (i) and (ii), we GET `""(3T_(i))/(4V_(1))=(2T_(f))/(3V_(2))` or `""T_(f)=9/8xx(V_(2))/(V_(1))xxT_(1)` `""=9/8xx5/4xx320=450K`