Question

A football was inflated to a gauge pressure of 1 bar when the ambient temperature was 15°C. When the game started next day, the air temperature at the stadium was 5°C. Assume that the volume of the football remains constant at $2500c{m}^3$.

Gauge pressure of air to which the ball must have been originally inflated so that it would be equal 1 bar gauge at the staduim is

• A. 2.23 bar
• B. 1.94 bar
• C. 1.07 bar
• D. 1.00 bar

Answer 1

The correct option is C 1.07 bar

(c)
If ${\rho }_{G1}=1bar=100kPa$
Absolute pressure,
${\rho }_1={\rho }_{G1}+{\rho }_{atm}=100+101.325$
$=201.325kPa$
$T_1=278K$
$T_2=288K$
At V = C
$\frac{{\rho }_2}{T_2}=\frac{{\rho }_1}{T_1}$
$\frac{\rho }{288}=\frac{201.325}{278}$
or $\rho =208.56kPa$
also $\rho ={\rho }_{G2}+{\rho }_{atm}$
$\therefore$ $208056={\rho }_{G2}+101.325$
or ${\rho }_{G2}=107.235kPa$
$=1.07bar$