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Chapter 3: Problem 30

Which of the following are units of power? (Pascal is a unit of pressure.) i. watt ii. kilowatt \(\mathrm{hr}\) iii. newton \(\mathrm{m} / \mathrm{s}\) iv. kilowatt hr/day v. pascal \(\mathrm{m}^3 / \mathrm{s}\) (A) i (B) i and ii (C) ii and iii (D) iv and \(v\) (E) i, iii, iv and \(v\)

Short Answer

Expert verified
(A) i only (B) i and iii only (C) i, ii, and iv only (D) ii, iii, and v only (E) i, iii, iv, and v Options: i. Watt (W) ii. Kilowatt-hour (kWh) iii. Newton meter per second (N m/s) iv. Kilowatt hour per day (kWh/day) v. Pascal meter cubed per second (Pa m³/s) Answer: (E) i, iii, iv, and v

Step by step solution

01

Analyze Option i

Watt (W) is the standard unit of power; it is equal to one joule per second (J/s). So, option i is a unit of power.
02

Analyze Option ii

Kilowatt-hour (kWh) is a unit of energy, not power. It represents the amount of energy consumed at a rate of 1,000 watts over one hour. Therefore, option ii is not a unit of power.
03

Analyze Option iii

Newton meter per second (N m/s) can be expressed as (kg m/s²)(m/s) = (kg m²/s³), which is equivalent to a joule per second (J/s), the same as a watt. Therefore, option iii is a unit of power.
04

Analyze Option iv

Kilowatt hour per day (kWh/day) can be expressed as (1000 J/s)(hr/day), and, by converting hours and days to seconds, we can simplify this to (1000 J/s)(3600 s/86400 s), which simplifies to (1000 J/s)(1/24). Thus, it is equivalent to (1000/24) J/s or (1000/24) W, which is a unit of power. Therefore, option iv is a unit of power.
05

Analyze Option v

Pascal meter cubed per second (Pa m³/s) can be expressed as (N/m²)(m³/s). By putting the units together, we have (kg m/s²)(m²/s), which simplifies to (kg m²/s³), the same as a watt. Therefore, option v is a unit of power.
06

Select the correct answer

Based on our analysis, options i, iii, iv, and v are units of power. The correct answer is (E) i, iii, iv, and v.

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