(a) A 1000 watt hour is kept on in a room whose dimensions are `5m xx 5m xx 3m`. Howmuch temperature of the room will rise after half an hour? Given the following data `:`
Heat capacity ofair at room temperature and 1 atm`= 0.71 Jg^(-1)K^(-1)`
Density ofair `= 1.22xx 10^(-3) g mL^(-1)`
(b) How much temperature of the room willrise if `25%` heat is lost by radiation ?

Explanation

(a) 1 Watt `= 1 J s^(-1)`
`:. `Heat evolved by 1000 W heaterin 30min. `= 100 xx 30 xx 60 J = 18 xx 10^(5) J`
Volume of the room ` 5 xx4 xx 3m^(3) = 60 m^(3) = 60 xx 10^(6) cm^(3) `
Density of air`=1.22 xx 10^(-3) g mL^(-1)`
Mass of air in the room`= ( 60xx 10^(6)) xx ( 1.22 xx 10^(-3)) g = 73.2 xx 10^(3)g`
Heat evolved by the heater `=` Heat absorbed by walls, roof and air inside.
`18 xx10^(5) J =( 5 xx 10^(4) xx Delta T ) + ( 73.2 xx 10^(3)) xx 0.71 xx Delta T`
`= ( 50000+ 51972 )Delta T`
`= 101972 Delta T = 1.01 972 xx 10^(5) DeltaT `
or `Delta T = ( 1.8 xx 10^(5))/( 1.01972 xx 10^(5)) = 17.65^(@) `
(b) If `25%` heat is lost by radiation, net heat available in the room
` = (75)/( 100) xx 18 xx 10^(5) J = 13.5 xx 10^(5) J` ,brgt `13.5 xx 10^(5) J = ( 5 xx 10^(4) xx Delta T ) + ( 73.2 xx 10^(3)) xx 0.71xx DeltaT`
or` Delta T =( 13.5 xx 10^(5))/( 1.01972xx 10^(5)) = 13.24^(@)`