(a) How much waste heat is produced by an electrical power station that uses 1.05 multiplied by 1014 J of heat input with an efficiency of 40.0%?
(b) What is the ratio of waste heat to work output?
(c) How much work is done?
η= 40% =>η =0.4
input heat Q₁=1.05•10¹⁴J
waste heat Q₂=0.6 Q₁=6.3•10¹³ J
Q₂/W=1.5
work W=0.4 Q₁=4.2•10¹³ J
To find the answers to these questions, we need to use the formulas related to efficiency, work, and waste heat in a power station.
(a) To calculate the amount of waste heat produced by the power station, we need to find the heat input and multiply it by (1 - efficiency).
Waste Heat = Heat Input × (1 - Efficiency)
Given:
Heat Input = 1.05 × 10^14 J
Efficiency = 40%
Waste Heat = 1.05 × 10^14 J × (1 - 0.40)
= 1.05 × 10^14 J × 0.60
= 6.30 × 10^13 J
Therefore, the power station produces 6.30 × 10^13 J of waste heat.
(b) To calculate the ratio of waste heat to work output, we divide the waste heat by the work output.
Ratio of Waste Heat to Work Output = Waste Heat / Work Output
Since there is no specific value given for the work output, we cannot find the exact ratio in this case.
(c) To determine the amount of work done, we use the equation:
Work = Heat Input × Efficiency
Given:
Heat Input = 1.05 × 10^14 J
Efficiency = 40%
Work = 1.05 × 10^14 J × 0.40
= 4.20 × 10^13 J
Therefore, the amount of work done by the power station is 4.20 × 10^13 J.