A cylinder closed at both ends is separated into two equal parts ( 45 cm each) by a piston impermeable to heat. Both the parts contain the same masses of gas at a temperature of 300 K and a pressure of 1 atm . If now the gas in one of the parts is heated such that the piston shifts by 5 cm , then the temperature and the pressure of the gas in this part after heating is

Step-by-step solution

Let the crossectional area of the cylinder is A . Initially Representing a closed cylinder separated by a piston The piston is shifted by 5   cm in the cylinder For 1, p 1 V 1 T 1 = p 2 V 2 T 2   ⇒   p V 300 = p 2 V + A x T 2 .....(i) For 2, p 1 V 1 = p 2 V 2   ⇒   p V = p 2 V - A x p 2 = p V V - A x ....(ii) From Equations (i) and (ii), p V 300 = p V V - A x ⋅ V + A x T 2 ⇒     T 2 = V + A x V - A x 300 = A 45 +A5 A 45 -A5 × 300 = 50 40 300 T 2 = 375