Question

A cylinder with a movable piston is filled at 24^oC with a gas that occupies 36.2cm³. If the maximum capacity of the cylinder is 65.2cm³, what is the highest temperature to which the cylinder can be heated at constant pressure without having the piston come out?

Answer 1

Ans. Given, the piston is moveable, i.e. the cylinder is at 1 atm pressure.

Now, Using pV= nRT                                        [24⁰C = 297.15 K; 36.2 cm³= 0.0362 L]

                n = (pV)/ (RT) = (1 atm x 0.0362 L) /

                or, n = (0.0362 atm L) / (24.38337 L atm mol^-1)

                or, n = 0.001485

Hence, number of moles of gas in the cylinder = 0.001485

The piston comes out the moment the pressure in the cylinder exceeds 1 atm.

So, calculate the temperature at which pressure becomes more than 1 atm, given V= 65.2 mL

Again, using pV= nRT

                1 atm x 0.0652 L = (0.001485 moles) x (0.08205746 L atm K^-1mol^-1 ) x T

                Or, T = (0.0652 L atm) / (0.000122 L atm K^-1) =534.4262295081967 K

                Or, T = 534.42 K = 261.27⁰C

Thus, 261.27⁰C is the maximum temperature till which the cylinder can be heated without the piston coming out.