Answer :
Answer : The time required is, 16.1 minutes.
Explanation :
First we have to calculate the amount of heat required to increase the temperature is:
[tex]Q=mC\Delta T\\\\Q=\rho VC\Delta T[/tex]
[tex](m=\rho V)[/tex]
where,
Q = amount of heat required = ?
m = mass
[tex]\rho[/tex] = density of air = [tex]1.20kg/m^3[/tex]
V = volume of air
C = specific heat of air = [tex]1006J/kg^oC[/tex]
[tex]\Delta T[/tex] = change in temperature = [tex]10.0^oC[/tex]
Now put all the given values in above formula, we get:
[tex]Q=\rho VC\Delta T[/tex]
[tex]Q=(1.20kg/m^3)\times (3.00m\times 5.00m\times 8.00m)\times (1006J/kg^oC)\times (10.0^oC)[/tex]
[tex]Q=1.449\times 10^6J[/tex]
Now we have to calculate the time required.
Formula used :
[tex]t=\frac{Q}{P}[/tex]
where,
t = time required = ?
Q = amount of heat required = [tex]1.449\times 10^6J[/tex]
P = power = 1500 W
Now put all the given values in above formula, we get:
[tex]t=\frac{1.449\times 10^6J}{1500W}[/tex]
[tex]t=966s\times \frac{1min}{60s}=16.1min[/tex]
Thus, the time required is, 16.1 minutes.