A cylinder of fixed capacity 44.8 litres contains helium gas at standard temperature and pressure. What is the amount of heat needed to raise the temperature of the gas in the cylinder by `15.0^(@)C` ? (`R= 8.31Jmol^(-1)K^(-1)`)

Explanation

Using the gas law `PV = muRT`, you can easily show that 1 mol of any (ideal) gas at standard temperature (273 K) and pressure (`1 "atm" = 1.01 x× 10^(5)` Pa) occupies a volume of 22.4 litres. This universal volume is called molar volume. Thus the cylinder in this example contains 2 mol of helium. Further, since helium is monatomic, its predicted (and observed) molar specific heat at constant volume, `C_(v) = (3//2) R`, and molar specific heat at constant pressure, `C_(p) = (3//2) R+R= (5//2) R`. Since the volume of р the cylinder is fixed, the heat required is determined by `C_(v)` Therefore,
`"Heat required" = "no. of moles" xx "molar specific heat" xx "rise in temperature"`
`= 2 xx 1.5R xx15.0= 45R`
`= 45 xx 8.31= 374J`