/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 16 (a) How much heat does an engine... [FREE SOLUTION] | 91影视

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Chapter 15: Problem 16

(a) How much heat does an engine with an efficiency of \(33.3 \%\) absorb in order to deliver \(1.00 \mathrm{kJ}\) of work? (b) How much heat is exhausted by the engine?

Short Answer

Expert verified
Question: An engine has an efficiency of 33.3% and delivers 1.00 kJ of work. Calculate the heat absorbed and the heat exhausted by the engine. Answer: The engine absorbs 3.00 kJ of heat and exhausts 2.00 kJ of heat.

Step by step solution

01

Recall the formula for efficiency

The efficiency of an engine is defined as the ratio of work output to the heat input. Mathematically, it can be written as: Efficiency = \(\frac{\text{Work output}}{\text{Heat input}}\)
02

Convert the efficiency to a decimal

The efficiency of the engine is given as \(33.3 \%\). To work with it in our calculations, we need to convert it into a decimal. To do this, divide the percentage by \(100\): Efficiency (as decimal) = \(\frac{33.3}{100} = 0.333\)
03

Rearrange the efficiency formula to find the heat input

We need to find the heat input to the engine, so rearrange the efficiency formula: Heat input = \(\frac{\text{Work output}}{\text{Efficiency}}\)
04

Calculate the heat input

Now, plug in the given values (work output = \(1.00 \mathrm{kJ}\), efficiency = \(0.333\)): Heat input = \(\frac{1.00 \mathrm{kJ}}{0.333} \approx 3.00 \mathrm{kJ}\) The engine absorbs \(3.00 \mathrm{kJ}\) of heat in order to deliver \(1.00 \mathrm{kJ}\) of work.
05

Recall the conservation of energy principle

According to the conservation of energy principle, the energy input to the engine is equal to the sum of its work output and the heat it exhausts: Heat input = Work output + Heat exhausted
06

Calculate the heat exhausted by the engine

Rearrange the conservation of energy formula to find the heat exhausted: Heat exhausted = Heat input - Work output Now, plug in the values we found before (heat input = \(3.00 \mathrm{kJ}\), work output = \(1.00 \mathrm{kJ}\)): Heat exhausted = \(3.00 \mathrm{kJ} - 1.00 \mathrm{kJ} = 2.00 \mathrm{kJ}\) The engine exhausts \(2.00 \mathrm{kJ}\) of heat.

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Most popular questions from this chapter

An engine works at \(30.0 \%\) efficiency. The engine raises a \(5.00-\mathrm{kg}\) crate from rest to a vertical height of \(10.0 \mathrm{m}\) at which point the crate has a speed of \(4.00 \mathrm{m} / \mathrm{s} .\) How much heat input is required for this engine?
List these in order of increasing entropy: (a) 0.01 mol of \(\mathrm{N}_{2}\) gas in a \(1-\mathrm{L}\) container at \(0^{\circ} \mathrm{C} ;\) (b) 0.01 mol of \(\mathrm{N}_{2}\) gas in a 2 -L container at \(0^{\circ} \mathrm{C} ;\) (c) 0.01 mol of liquid \(\mathrm{N}_{2}\).
List these in order of increasing entropy: (a) 1 mol of water at $20^{\circ} \mathrm{C}\( and 1 mol of ethanol at \)20^{\circ} \mathrm{C}$ in separate containers; (b) a mixture of 1 mol of water at \(20^{\circ} \mathrm{C}\) and 1 mol of ethanol at \(20^{\circ} \mathrm{C} ;\) (c) 0.5 mol of water at \(20^{\circ} \mathrm{C}\) and 0.5 mol of ethanol at \(20^{\circ} \mathrm{C}\) in separate containers; (d) a mixture of 1 mol of water at $30^{\circ} \mathrm{C}\( and 1 mol of ethanol at \)30^{\circ} \mathrm{C}$.
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A fish at a pressure of 1.1 atm has its swim bladder inflated to an initial volume of \(8.16 \mathrm{mL}\). If the fish starts swimming horizontally, its temperature increases from \(20.0^{\circ} \mathrm{C}\) to $22.0^{\circ} \mathrm{C}$ as a result of the exertion. (a) since the fish is still at the same pressure, how much work is done by the air in the swim bladder? [Hint: First find the new volume from the temperature change. \(]\) (b) How much heat is gained by the air in the swim bladder? Assume air to be a diatomic ideal gas. (c) If this quantity of heat is lost by the fish, by how much will its temperature decrease? The fish has a mass of \(5.00 \mathrm{g}\) and its specific heat is about $3.5 \mathrm{J} /\left(\mathrm{g} \cdot^{\circ} \mathrm{C}\right)$.
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