Question

A sealed cylinder of gas contains nitrogen gas at 1.00 ✕ 103 kpa pressure and a temperature of 19°c. the cylinder is left in the sun, and the temperature of the gas increases to 46°c. what is the new pressure in the cylinder?

Answer 1

According to Gay -Lussac’s law (at constant volume, as pressure increases, temperature increases)

`(P_(1) )/(T_(1) ) =(P_(2) )/( T_(2) )`

Given,
`P_(1) =1.00* 10^(3) \ kPa` ,
`T_(1) =19^o C = (19 +273 ) = 292 \ k` and
`T_(2) =46^o C = (46 +273 ) = 319 \ k`

Substituting these values, in above formula, we get

`(1.00* 10^(3) \ kPa)/(292 \ K) = (P_(2) )/(319 \ K)\\\\ P_(2) =(1.00* 10^(3) \ kPa * 319 K)/(292K) = 1.09 * 10^3 \ kPa`.

Thus, the new pressure in the cylinder is
`1.09 * 10^3 \ kPa`.