A sample of air weighing `1.18 g` occupies `1.0 xx 10^(3) cm^(3)` when kept at `300 K and 1.0 xx 10^(5)` pa. When `2.0 cal` of heat is added to it constant volume, its temperature increases by `1^@C`. Calculate the amount if heat needed to increases the temperature of air by `1^@C` at constant pressure if the mechanical equivalent of heat si `4.2 xx 10^(-1)` . Assume that air behaves as an ideal gas.

Explanation

`m=1.18g`
`V=1xx10^(3) cm^(3)= 1L`
`T=300K`, `P=10^(5) Pa`
`PV =nRT`
or `n=(PV)/(RT)` `[10^(5)Pa=1atm.]`
implies `n=(1)/(8.2xx10^(-2)xx3xx10^(2)`
implies `=(1)/(8.2xx3)=1/24.6`
Now, `C_v =1/nxx2 = 24.6 xx 2 =49.2`
`C_p =R+C_v = 1.987 +49.2`
`=51.187`
`Q=nC_p dT`
`=(1)/(24.6)xx 51.187xx1`
`=2.08 cal`.