Convert each of the following pressures to the units specified: a 140kPa to Pa b 92000Pa to kPa c 4.24atm to mmHg and Pa d 120kPa to mmHg, atm and bar e 1400mmHg to atm, Pa and bar f 80000Pa to atm, mmHg and bar
The Correct Answer and Explanation is :
Let’s go step by step to convert each pressure value to the required units. We will use the following conversion factors for the calculations:
- Pressure conversions:
- ( 1 \text{ kPa} = 1,000 \text{ Pa} )
- ( 1 \text{ atm} = 101,325 \text{ Pa} )
- ( 1 \text{ atm} = 760 \text{ mmHg} )
- ( 1 \text{ mmHg} = 133.322 \text{ Pa} )
- ( 1 \text{ bar} = 100,000 \text{ Pa} )
Now, let’s solve the problems:
(a) Convert 140 kPa to Pa:
[
140 \text{ kPa} = 140 \times 1,000 \text{ Pa} = 140,000 \text{ Pa}
]
(b) Convert 92,000 Pa to kPa:
[
92,000 \text{ Pa} = \frac{92,000}{1,000} \text{ kPa} = 92 \text{ kPa}
]
(c) Convert 4.24 atm to mmHg and Pa:
- To mmHg:
[
4.24 \text{ atm} = 4.24 \times 760 \text{ mmHg} = 3,222.4 \text{ mmHg}
] - To Pa:
[
4.24 \text{ atm} = 4.24 \times 101,325 \text{ Pa} = 429,627 \text{ Pa}
]
(d) Convert 120 kPa to mmHg, atm, and bar:
- To mmHg:
[
120 \text{ kPa} = 120 \times 1,000 \text{ Pa} = 120,000 \text{ Pa}
]
[
120,000 \text{ Pa} = \frac{120,000}{133.322} \text{ mmHg} \approx 899.4 \text{ mmHg}
] - To atm:
[
120,000 \text{ Pa} = \frac{120,000}{101,325} \text{ atm} \approx 1.184 \text{ atm}
] - To bar:
[
120,000 \text{ Pa} = \frac{120,000}{100,000} \text{ bar} = 1.2 \text{ bar}
]
(e) Convert 1400 mmHg to atm, Pa, and bar:
- To atm:
[
1400 \text{ mmHg} = \frac{1400}{760} \text{ atm} \approx 1.842 \text{ atm}
] - To Pa:
[
1400 \text{ mmHg} = 1400 \times 133.322 \text{ Pa} = 186,652.8 \text{ Pa}
] - To bar:
[
186,652.8 \text{ Pa} = \frac{186,652.8}{100,000} \text{ bar} = 1.866 \text{ bar}
]
(f) Convert 80,000 Pa to atm, mmHg, and bar:
- To atm:
[
80,000 \text{ Pa} = \frac{80,000}{101,325} \text{ atm} \approx 0.790 \text{ atm}
] - To mmHg:
[
80,000 \text{ Pa} = \frac{80,000}{133.322} \text{ mmHg} \approx 600.3 \text{ mmHg}
] - To bar:
[
80,000 \text{ Pa} = \frac{80,000}{100,000} \text{ bar} = 0.8 \text{ bar}
]
Summary of answers:
- (a) 140 kPa = 140,000 Pa
- (b) 92,000 Pa = 92 kPa
- (c) 4.24 atm = 3,222.4 mmHg = 429,627 Pa
- (d) 120 kPa = 899.4 mmHg = 1.184 atm = 1.2 bar
- (e) 1400 mmHg = 1.842 atm = 186,652.8 Pa = 1.866 bar
- (f) 80,000 Pa = 0.790 atm = 600.3 mmHg = 0.8 bar
Explanation:
To convert pressure units, we use predefined relationships between the various units. Converting between units of pressure like kPa, Pa, atm, mmHg, and bar relies on knowing these relationships, which are based on historical measurements and physical constants. The unit Pascal (Pa) is the SI unit for pressure, while other units such as atm, mmHg, and bar are used in different contexts or regions. By applying simple multiplication or division using the appropriate conversion factors, you can easily switch between these units. For example, multiplying by 1,000 converts kPa to Pa, and dividing by 101,325 converts Pa to atm.