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Chapter 10: Problem 17

The amount of heat required will be minimum when a body is heated through (A) \(1 \mathrm{~K}\) (B) \(1^{\circ} \mathrm{C}\) (C) \(1^{\circ} \mathrm{F}\) (D) It will be the same in all the three cases

Short Answer

Expert verified
(C) \(1^{\circ} \mathrm{F}\)

Step by step solution

01

Understand the units of temperature

The exercise mentions three temperature scales - Kelvin denoted by K, Celsius denoted by \(^{\circ} \mathrm{C}\), and Fahrenheit denoted by \(^{\circ} \mathrm{F}\). Of these, Kelvin and Celsius have the same magnitude, i.e., a change of \(1^{\circ} \mathrm{C}\) is equivalent to a change of \(1 \mathrm{K}\). However, Fahrenheit is a different scale and a change of \(1^{\circ} \mathrm{F}\) is not equivalent to a change of \(1 \mathrm{K}\) or \(1^{\circ} \mathrm{C}\).
02

Analyze the question

The question asks which temperature scale would require the minimum amount of heat to change the body's temperature. Since the Fahrenheit scale has a smaller magnitude compared to the Kelvin and Celsius scales, a change of \(1^{\circ} \mathrm{F}\) would require less heat than a change of \(1 \mathrm{K}\) or \(1^{\circ} \mathrm{C}\).
03

Final Answer

After understanding the concept of temperature scales and analyzing the question, we can conclude that option (C) \(1^{\circ} \mathrm{F}\) is the correct answer as it will require the least amount of heat for a body to be heated through \(1^{\circ} \mathrm{F}\).

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Key Concepts

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

Temperature Scales
Temperature scales help us quantify how hot or cold an object is. They provide a consistent way to measure temperature differences across various activities and scientific disciplines.
Each scale has its own unit and method of measurement, ensuring it is suitable for specific purposes. Temperature is an important measure in understanding heat transfer, which concerns how heat moves from hotter objects to cooler ones.
There are three main temperature scales used worldwide: Kelvin, Celsius, and Fahrenheit.
  • Kelvin is often used in scientific settings and is the base unit of temperature in the International System of Units (SI).
  • Celsius is commonly used around the world, especially for weather and everyday temperature measurements.
  • Fahrenheit is primarily used in the United States for measuring atmospheric temperature.
Understanding these temperature scales allows us to convert temperatures and compare them across different contexts.
Kelvin
The Kelvin scale is the most scientific temperature scale. It is used mainly in physics and chemistry due to its absolute nature.
Kelvin measurements are directly related to the laws of thermodynamics. The Kelvin scale starts at absolute zero, the point at which no further thermal energy can be removed from a substance.
Absolute zero is 0 Kelvin or -273.15 degrees Celsius, which makes it very suitable for scientific equations and calculations.
  • Units in the Kelvin scale are simply called Kelvins, abbreviated as K.
  • The Kelvin scale does not use degree signs like Celsius and Fahrenheit do.
  • Converting from Celsius to Kelvin is easy: just add 273.15 to the Celsius temperature.
When dealing with problems of heat transfer in scientific studies, Kelvin serves as a reliable scale due to its direct connection to absolute thermal energy.
Celsius
The Celsius scale is widely used across the globe for measuring everyday temperatures, such as the weather or room temperatures. It is part of the metric system, which is why it is so popular internationally.
The Celsius scale is based on the freezing and boiling points of water, being 0 degrees Celsius and 100 degrees Celsius respectively.
  • Its unit is the degree Celsius, denoted as \(^{\circ}\mathrm{C}\).
  • This scale is easy to understand because of its direct relation to natural phenomena like the freezing and boiling of water.
  • Celsius can be converted to Kelvin by adding 273.15 to the Celsius value.
For day-to-day activities and activities related to climate and weather, Celsius remains the most convenient choice.
Fahrenheit
The Fahrenheit scale is primarily used in the United States and some Caribbean countries. On this scale, water freezes at 32 degrees Fahrenheit and boils at 212 degrees Fahrenheit.
It provides a slightly more granular approach to temperature measurement compared to Celsius, which can be seen in the finer gradations between the freezing and boiling points of water.
  • Temperatures are measured in degrees Fahrenheit, represented as \(^{\circ}\mathrm{F}\).
  • The Fahrenheit scale is known for providing detailed temperature readings, making it beneficial for precise weather forecasts and temperature descriptions.
  • To convert Celsius to Fahrenheit, you can use the formula \(\frac{9}{5} \times (\text{Celsius temperature}) + 32 \).
While not as universally adopted as Celsius, Fahrenheit remains important for specific regions and applications.

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Most popular questions from this chapter

Gulab jamuns (assumed to be spherical) are to be heated in an oven. They are available in two sizes, one twice bigger (in radius) than the other. Pizzas (assumed to be discs) are also to be heated in oven. They are also in two sizes, one twice bigger (in radius) than the other. All four are put together to be heated to oven temperature. Choose the correct option from the following. (A) Both size gulab jamuns will get heated in the same time. (B) Smaller gulab jamuns are heated before bigger ones. (C) Smaller pizzas are heated before bigger ones. (D) Bigger pizzas are heated before smaller.

An aluminium sphere is dipped into water. Which of the following is true? (A) Buoyancy will be less in water at \(0^{\circ} \mathrm{C}\) than that in water at \(4^{\circ} \mathrm{C}\) (B) Buoyancy will be more in water at \(0^{\circ} \mathrm{C}\) than that in water at \(4^{\circ} \mathrm{C}\) (C) Buoyancy in water at \(0^{\circ} \mathrm{C}\) will be same as that in water at \(4^{\circ} \mathrm{C}\) (D) Buoyancy may be more or less in water at \(4^{\circ} \mathrm{C}\) depending on the radius of the sphere

Mark the correct options (A) A system \(X\) is in thermal equilibrium with \(Y\) but not with \(Z\). The system \(Y\) and \(Z\) may be in thermal equilibrium with each other. (B) A system \(X\) is in thermal equilibrium with \(Y\) but not with \(Z\). The system \(Y\) and \(Z\) are not in thermal equilibrium with each other. (C) A system \(X\) is neither in thermal equilibrium with \(Y\) nor with \(Z\). The systems \(Y\) and \(Z\) must be in thermal equilibrium with each other. (D) A system \(X\) is neither in thermal equilibrium with \(Y\) nor with \(Z\). The systems \(Y\) and \(Z\) may be in thermal equilibrium with each other.

A pendulum clock loses 12 s a day if the temperature is \(40^{\circ} \mathrm{C}\) and gains \(4 \mathrm{~s}\) day if the temperature is \(20^{\circ} \mathrm{C}\). The temperature at which the clock will show correct time, and the co-efficient of linear expansion \((\alpha)\) of the metal of the pendulum shaft are respectively. [2016] (A) \(60^{\circ} \mathrm{C} ; \alpha=1.85 \times 10^{-4} /{ }^{\circ} \mathrm{C}\) (B) \(30^{\circ} \mathrm{C} ; \alpha=1.85 \times 10^{-3} /{ }^{\circ} \mathrm{C}\) (C) \(55^{\circ} \mathrm{C} ; \alpha=1.85 \times 10^{-2} /{ }^{\circ} \mathrm{C}\) (D) \(25^{\circ} \mathrm{C} ; \alpha=1.85 \times 10^{-5} /{ }^{\circ} \mathrm{C}\)

A substance of mass \(m \mathrm{~kg}\) requires is power input of \(P\) watts to remain in the molten state at its melting point. When the power is turned off, the sample completely solidifies in time \(t\) second. What is the latent heat of fusion of the substance? (A) \(\frac{P m}{t}\) (B) \(\frac{P t}{m}\) (C) \(\frac{m}{P t}\) (D) \(\frac{t}{P m}\)
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