TICKET 1-29 1. The flue gas in the chimney is cooled at a constant pressure from 340^circ C to 290^circ C How many times smaller must the cross-section area of the upper chimney end be than the cross -section area of the lower end? The gas velocity in the chimney is maintained the

To solve this problem, we can use the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature and inversely proportional to its volume. Since the pressure is constant, we can use the formula:<br /><br />\[ \frac{V_1}{V_2} = \frac{T_1}{T_2} \]<br /><br />where \( V_1 \) and \( V_2 \) are the volumes of the gas at the lower and upper ends of the chimney, respectively, and \( T_1 \) and \( T_2 \) are the temperatures at the lower and upper ends of the chimney, respectively.<br /><br />Given that the temperature decreases from \( 340^{\circ}C \) to \( 290^{\circ}C \), we can substitute these values into the formula:<br /><br />\[ \frac{V_1}{V_2} = \frac{340}{290} \]<br /><br />Simplifying the fraction, we get:<br /><br />\[ \frac{V_1}{V_2} = \frac{34}{29} \]<br /><br />This means that the volume of the gas at the lower end of the chimney is \( \frac{34}{29} \) times larger than the volume of the gas at the upper end of the chimney.<br /><br />Since the cross-section area of the chimney is directly proportional to its volume, the cross-section area of the upper chimney end must be \( \frac{29}{34} \) times smaller than the cross-section area of the lower end.