At what temperature does this occur?

Question

Some hydrogen gas is enclosed within a chamber being held at 200degrees celcius whose volume is 0.025 m^3. Initially, the pressure in the gas is 1.50 * 10^6 Pa (about 1.5atm ). The chamber is removed from the heat source and allowed to cool until the pressure in the gas falls to .95 *10^6 Pa.

Answer 1

The combined gas laws of Charles, Boyle and Gay-Lussac states that:

P1V1/T1 = P2V2/T2

Since V1 = V2 we get

P1/T1 = P2/T2
so
T2 = T1*P2/P1 = (200+273)K * 0.95e6 Pa / 1.5e6Pa
T2 = 299.6 K
T2 = (299.6-273) Celsius = 26.6 degree Celsius

Answer 2

Assuming the Volume is constant.....

200 Celsius = 473 Kelvin.

Pressure decrease is-:

Ratio of Pressure = 1 : 0.6333

Therefore Temp = 473 x 0.6333 = 299.55 Kelvin (About 27 degrees celsius)