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Chapter 1: Problem 35

Convert the following temperatures from \({ }^{\circ} \mathrm{C}\) to \(\mathrm{K}:\) (a) \(21^{\circ} \mathrm{C}\). (b) \(-40^{\circ} \mathrm{C}\), (c) \(500^{\circ} \mathrm{C}\), (d) \(0^{\circ} \mathrm{C}\), (e) \(100^{\circ} \mathrm{C}\), (f) \(-273.15^{\circ} \mathrm{C}\).

Short Answer

Expert verified
21掳C = 294.15 K, -40掳C = 233.15 K, 500掳C = 773.15 K, 0掳C = 273.15 K, 100掳C = 373.15 K, -273.15掳C = 0 K.

Step by step solution

01

Understand the Conversion Formula

To convert from Celsius (掳C) to Kelvin (K), use the formula: \[ K = 掳C + 273.15 \]
02

Convert 21掳C to K

Applying the formula: \[ K = 21 + 273.15 = 294.15 \] Thus, \( 21^{\bullet}C = 294.15 K \)
03

Convert -40掳C to K

Applying the formula: \[ K = -40 + 273.15 = 233.15 \] Thus, \( -40^{\bullet}C = 233.15 K \)
04

Convert 500掳C to K

Applying the formula: \[ K = 500 + 273.15 = 773.15 \] Thus, \( 500^{\bullet}C = 773.15 K \)
05

Convert 0掳C to K

Applying the formula: \[ K = 0 + 273.15 = 273.15 \] Thus, \( 0^{\bullet}C = 273.15 K \)
06

Convert 100掳C to K

Applying the formula: \[ K = 100 + 273.15 = 373.15 \] Thus, \( 100^{\bullet}C = 373.15 K \)
07

Convert -273.15掳C to K

Applying the formula: \[ K = -273.15 + 273.15 = 0 \] Thus, \( -273.15^{\bullet}C = 0 K \)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Celsius to Kelvin
The conversion from Celsius to Kelvin might look challenging at first, but it's actually quite simple. Both scales are used to measure temperature, but Kelvin is usually employed in scientific contexts.

To convert any temperature from Celsius (掳C) to Kelvin (K), you always add the same number: 273.15. This value is the difference between the freezing point of water in Celsius (0掳C) and in Kelvin (273.15K). So, the general formula for this conversion is:

K = 掳C + 273.15

For instance, to convert 21掳C to Kelvin, just apply the formula:

K = 21 + 273.15 = 294.15

Therefore, 21掳C equals 294.15K. It's that simple!
Thermodynamic Temperature Scale
The thermodynamic temperature scale, commonly known as the Kelvin scale, is rooted in the principles of thermodynamics, making it ideal for scientific purposes.

Unlike the Celsius scale, which designates the freezing point of water at 0掳 and the boiling point at 100掳, the Kelvin scale starts from absolute zero. At absolute zero (0K), molecular motion theoretically ceases.

This scale is called a 'thermodynamic' scale because it directly relates to energy. One Kelvin is defined by the fixed Boltzmann constant, linking temperature with energy. Hence, Kelvin measurements are essential in fields like physics and chemistry.

For example:
  • Absolute zero (0K) is -273.15掳C
  • Freezing point of water (273.15K) is 0掳C
  • Boiling point of water (373.15K) is 100掳C
These points highlight how the Kelvin scale simplifies and standardizes temperature measurement in scientific research.
Temperature Calculation Steps
Mastering temperature calculations is essential for various scientific studies and everyday tasks. Here's how to convert Celsius to Kelvin in easy steps:

1. **Understand the Conversion Formula**
The key formula is: K = 掳C + 273.15
This shows that converting any Celsius value to Kelvin requires adding 273.15.

2. **Apply the Formula**
Follow these calculations for some common temperatures:
  • 21掳C to K: K = 21 + 273.15 = 294.15
  • -40掳C to K: K = -40 + 273.15 = 233.15
  • 500掳C to K: K = 500 + 273.15 = 773.15
  • 0掳C to K: K = 0 + 273.15 = 273.15
  • 100掳C to K: K = 100 + 273.15 = 373.15
  • -273.15掳C to K: K = -273.15 + 273.15 = 0
By following these steps, you can convert any Celsius temperature to Kelvin accurately. Understanding this allows you to better grasp scientific studies and experiments involving temperature.

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Most popular questions from this chapter

In severe head-on automobile accidents, a deceleration of \(60 \mathrm{~g}\) 's or more \(\left(1 \mathrm{~g}=9.81 \mathrm{~m} / \mathrm{s}^{2}\right)\) often results in a fatality. What force, in \(\mathrm{N}\), acts on a child whose mass is \(22.7 \mathrm{~kg}\), when subjected to a deceleration of \(60 \mathrm{~g}\) 's?

Steam enters the first turbine stage of a vapor power plant with reheat and regeneration at \(12.4 \mathrm{MPa}, 590^{\circ} \mathrm{C}\) and expands in five stages to a condenser pressure of \(6.9 \mathrm{kPa}\). Reheat is at \(690 \mathrm{kPa}\) to \(538^{\circ} \mathrm{C}\). The cycle includes three feedwater heaters. Closed heaters operate at \(4.1 \mathrm{MPa}\) and \(1.1 \mathrm{MPa}\), with the drains from each trapped into the next lower-pressure feedwater heater. The feedwater leaving each closed heater is at the saturation temperature corresponding to the extraction pressure. An open feedwater heater operates at \(0.14 \mathrm{MPa}\). The pumps operate isentropically, and each turbine stage has an isentropic efficiency of \(88 \%\). (a) Sketch the layout of the cycle and number the principal state points. (b) Determine the thermal efficiency of the cycle. (c) Determine the heat rate, in \(\mathrm{kJ} / \mathrm{kW} \cdot \mathrm{h}\). (d) Calculate the mass flow rate into the first turbine stage, in \(\mathrm{kg} / \mathrm{h}\), for a net power output of \(3.2 \times 10^{9} \mathrm{~kJ} / \mathrm{h}\).

Water is the working fluid in an ideal Rankine cycle with reheat. Superheated vapor enters the turbine at \(8 \mathrm{MPa}\), \(440^{\circ} \mathrm{C}\), and the condenser pressure is \(8 \mathrm{kPa}\). Steam expands through the first- stage turbine to \(0.5 \mathrm{MPa}\) and then is reheated to \(440^{\circ} \mathrm{C}\). Determine for the cycle (a) the rate of heat addition, in \(\mathrm{kJ}\) per \(\mathrm{kg}\) of steam entering the first-stage turbine. (b) the thermal efficiency. (c) the rate of heat transfer from the working fluid passing through the condenser to the cooling water, in kJ per \(\mathrm{kg}\) of steam entering the first-stage turbine.

In Bangladesh, unsafe levels of arsenic, which is a tasteless, odorless, and colorless poison, are present in undergroundwells providing drinking water to millions of people living in rural areas. The task is to identify affordable, easy-to-use treatment technologies for removing arsenic from their drinking water. Technologies considered should include, but not be limited to, applications of smart materials and other nanotechnology approaches. Write a report including at least three references

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